What's a great minigame within another game?

Probably not what you are asking for, but the character creation process in the Traveller ttRPG is a great mini game. You basically take a person from 18 to however old you want, and their life path is dictated by your choices and random dice outcomes. It's a lot of fun. You can end up with a retired admiral, a prisoner or criminal, psionic, etc. Going through this process with a table of friends let's you build in rich fun connections along the way. The actual RPG then starts with mature, connected characters with a history, instead of 4 randos meeting in a tavern. In the classic Traveller you can even die in character creation. Current iterations removed the death component but you can be maimed from accidents in your career and start the game with a mountain of medical debt.

Not a minigame, but Maniac Mansion being within The Day of the Tentacle is probably my fav.

Treedude in superhot
And... Umm
Mario party

I thought of another one. There is a minigame in Xenoblade Chronicles 2 called Tiger! Tiger that is great. it is basically an arcade game where getting certain scores gives you credits that can be redeemed for upgrades for some characters. The minigame is randomized and has three different difficulty tiers and is overall really well done.

Not sure if it will count, but the Ancient Cave in Lufia 2 (SNES) was a game in and of itself. It was basically a roguelike dungeon. 100 random floors, it reverts you to level 1 and there were rare special items you could sometimes find in runs that could be brought back in. Beating the Ancient Cave is much, much harder and more rewarding than beating the game itself (storyline aside).

The minigames in shenmue/yakuza. They are literally full games.

The hunting game in Oregon Trail.

Pretty much every minigame in Majora's Mask is making you forget the world is ending

The full 4K version of Timesplitters 2 inside Homefront: The Revolution, but you have to play something like 75% of Homefront to reach it. I'll reach it one of these days.

Didn’t rocket league originate from a minigame ?
- No, it's the sequel to Supersonic Acrobatic Rocket Powered Battle Cars

Caravan from Fallout: New Vegas has a notoriously bad tutorial, but is easy enough to grasp and fun as an early-game money source. Would have benefited from a Gwent-style sidequest chain.

Ratchet and Clank: Up Your Arsenal had a side scrolling Captain Quark game that was quite good

Let's be real, Witcher 3 is just a Gwent launcher.
Also I've definitely played more Pazaak than KOTOR.
- In another life I wouldn't understand a word of these sentences lol
- I fucking love Gwent AND the fact that it’s horribly unbalanced (in The Witcher 3)
- Puuure pazaak
- I literally could never understand how to play Pazaak. To me it's just a weird version of Blackjack
  
  So you do understand it.
- I honestly don't like Gwent. Maybe never got into it enough.

The cornfield photo minigame in mario party ds

Playing Receiver in Receiver 2 was a fun surprise.

Geometry Wars in Project Gotham Racing 2.

The Chao racing from Sonic Adventure on the dream cast. You could take the memory card out and use it as a tamagotchi to care for the little guy and make it train so it gets faster and stronger in the real game.
It got no better than that.

The mini pinball game, at the top-right of the Family Guy pinball table(2007).
It is fast paced and well put together.
- That really makes me laugh and cry

Demontower, found within Night in the Woods. That could easily be a standalone short game

Triple triad card game from FF8? Also the card game in FF9, I forgot which is which.
- I came to mention this one! I loved that card game as a kid!
- I loved the FF8 card game. It was so sad that you had to choose to used up some cards if you wanted some equipments if I recall correctly. It would be nice to not have to choose to keep all cards or have all equipments os spells
  
  If you liked it enough, you could win another copy after you refined it by playing against the right people. I think there was only one card you couldn't get back again, and all the rest were fair game.

I loved the Chao Garden in the Sonic Adventure games.
- YES YOU KNOW IT
- Sonic Adventure 2 on Dreamcast was peak Sonic. Those things in the controller had a minigame within a minigame for extra costumes and food for the chao.

the game.
- Fk I lost

Triple triad from Final Fantasy 8.
- Triple triad + Card mod ability = broken game
  It might have had a factor in my not enjoying the Triple Triad mini game, as I sometimes get bogged down in just collecting cards to convert into spells and items. Also, the Queen of Cards is a huge pain. And the CC Club sidequest.
  
  I loved Triple Triad, and loved the way it broke the game!
  Shout out to all the hours I wasted soft resetting so I could eliminate the Random rule from Ellone. Honorable mention to the Laguna card, which refined into 100 Heroes and made every single fight after it complete child's play.
  
  Never bothered with Queen of Cards quest, as the walkthrough of that is... Sizable, to say the least. Also, there's only one relatively decent reward out of it (Doomtrain).
  As for CC: they are a source of all rare cards besides the ones Queen has. Thus, if you want to have Vit/Str/HP Ups - they're your best bet (also, getting enough of those makes Omega Weapon fight a breeze, you can reliably kill it without ever reaching Megido Flame and foregoing Holy War usage).
  But yeah... Triple Triad is fun, especially since it translates to sth that will impact your game.
  EDIT: also, you can get 3x100 Flare on your entire party on the first disc, but it's a major PITA to get (iirc, 300 Red Dragon cards, so good fuckin' luck). So yeah... Triple Triad brekas the game if you have the patience for it 😄
  EDIT 2: also also, Queen of Cards is available at the crash site on Disc 3 as well

I think DOOM Eternal has DOOM 2 inside of it... which then has ~~shatfenfrude~~ Wolfenstein inside of it. (ignore the spelling 😅)
edit: I forgot the name and accidentally tried to type the German word for laughing

It’s always fishing.
- Loved the fishing in FF15.

Maniac Mansion: day of the tentacle includes the full first maniac Mansion game on weird Ed's computer in the room with him and the hamster
EverQuest /gems and /pizza
- I had a lot more trouble with Maniac Mansion than DotT, I always got all my characters thrown in the dungeon. My favorite thing about it, at least the version on Weird Ed Edison's computer, was that it played music using the pc speaker, which is now a concept lost to time.

Who are you so wise in the ways of gwent?

Yakuza games are the only good Mahjong simulator. I’ve always thought Sega/RGK Studios should release a standalone one based on Yakuza.
All other Mahjong games are shitty western mahjong match tile games.

Sonic Adventure 2 has a pretty decent adventure platformer built into it
- Yeah, Chao Garden 2 Battle had some really amazing minigames. One of the best was the ability to play as Sonic or Shadow, and experience an entire plotline. Lots of players missed it almost entirely, because they were just too wrapped up in the main Chao Garden game to bother with the Light/Dark story stuff.

Blitzball Final Fantasy X
- A really divisive minigame, to be sure. My wife and I both hated blitzball, (I save-scummed to get Wakka’s ultimates ASAP, then never touched it again) but my buddy probably sank 150 hours into it during his first play through.
- I always sucked at blitzball

The Wolfenstein 3D minigame contained within Wolfenstein The New Order is probably the best one I've come across. I may be biased though since Wolfenstein 3D is probably one of my Top 5 all-time favorite games.
- In DOOM Eternal you can play through all of DOOM and DOOM 2 at the Slayer’s desk in the fortress. I dig that
  
  Everything runs Doom, even Doom!
  
  That's a really nice touch

I honestly really liked the Zen garden in Plants vs Zombies

I would just play Caravan if it didn't involve walking across the Mojave each time. Actually I'll walk just to play more Caravan.

borderlands science in borderlands 3 is probably my all time favourite mini-game in a video game

The surprisingly deep copy of Balatro in "Dave the Diver" is pretty good.

I always thought it was cool that you could play the original maniac mansion in day of the tentacle.

Karaoke, disco, cabaret club, pool, taxi racing, Space Harrier, kart racing, mahjong, poker, koi koi, business management, bowling, pocket circuit racing, spear fishing, piss contest, and of course fishing, all from the Like a Dragon series.

I like Knucklebones in Cult of the Lamb.

The fishing minigame from Breath of Fire 4. There's just something that's both simple and relaxing, as well as complex and engaging in that minigame. Even better, it's not a requirement to finish the game.
And then there's the fishing minigame on Stardew Valley.
- I enjoy the Stardew fishing lol
- Have you ever tried fishing?
  
  In real life? Nope. I don't think I have the patience for that, sitting perfectly still for hours on end. I would probably enjoy the scenery and the vibe though.

The tile placement game in Satisfactory is worth a mention. I never fully understood the points system, so I never really rode the game to decent scores, but it was a fun break from the vast size of the rest of the game.

Nobody mentioned Yakuza? Any modern game in the series? (Edit: Ok, one guy did)
A guilty pleasure of mine is Majima Construction from Yakuza Kiwami 2, which is one if the few RTS I like. It's unbalanced, and not even functioning properly, but it's simple fun. I associate most RTS with commanding large squads of units and resource management, and a watered down version with few specific characters and one/two resources felt like a less overwhelming entry point into the genre.

Astro Chicken (Space Quest III).

I have a love/hate relationship with Nethack's Sokoban levels.

Any love for DOOM 3’s Super Turbo Turkey Puncher 3? It was so dumb but I will admit to loving the way you interact with computers and terminals in DOOM 3

Legend of the Mystical Ninja has a Gradius style video game inside of it that was so good that when I quit playing it I had completely forgot I was inside another video game.
Mario Party 5 has a side game (not a mini game) called Card Party that is good enough to be its own mobile game.

There's a pretty good Solitaire game built into the Zachtronics game Shenzhen IO.
- Almost every Zachtronics game had some kind of solitaire. There’s an android app that has a collection of them.
  
  I don't remember one in TIS-100 or Infinifactory.

Earthborn in Eastward. It's a rogue like turn based rpg, and it's sick. Also you can use money you collect in Eastward to buy capsules that contain items that you can use inside Earthborn. Really cool idea executed perfectly. I played more of Earthborn than I did Eastward.
- Eastward is one of my favorite games I've ever played. My only significant criticism is that I spent most of the game looking forward to how all the loose ends to the story would be explained and tied together and then it just ended without that really happening.

That arcade shooter in Blades of Steel
- Hell yes.
  It makes me so mad that Namco patented load screen minigames for long enough that load screens have kinda gotten scarce and short enough that we don’t need the time waster anymore.

I hate minigames, the only one i tolerated was Gwent in Witcher 3.
- Same. I’m playing GTA San Andreas on mobile (through Netflix if you interested) and while the game holds up, all the minigames suck ass. I’m likely not going to complete a single one. Maybe I’ll cave and do burglaries for infinite sprint, but probably not.

I loved the Showtime crashes in Burnout Paradise. I know most people would say that it was a sorry excuse for a replacement to the Crash mode that came before in the previous Burnout games, but I never played any other than Paradise so I can’t compare

Burger Flipper in Selaco.
You need to find a datapad with the game on it, and it's just a stupid auto-clicker, but damn if it doesn't scratch that itch in the monkey brain for "number go up."
Plus, Selaco, the base game, is really damn fun.

Don't know if it would count since it's used in a couple levels, I think, but PVZ Reflourished, Caliginous Carnival. The levels where you essentially have to pay attention to the zombies beneath the hats and guess which is the weaker one in order to make the spawns easier to deal with. Rinse and repeat multiple rounds until you win. Would absolutely love to see that done more.
Also, along the lines of PVZ, iZombie is definitely up there for my favorite minigame in the series and in general. It absolutely sucks both versions of PVZ2 killed it (unless I'm wrong and the Chinese version still has the old PVP mode, but even then wasn't nearly as fun as the original minigame, nor anywhere near as balanced when half the time you'd find other players had level 4/5 plants that instantly destroy everything in 0.001 nanoseconds).

Arcomage of course!