The US gets 1/5 of its power from nuclear energy, and produces 2,000 metric tons of nuclear waste per year – only enough to fill about half of the volume of an olympic-sized swimming pool (and about the same weight as 10 wind turbines).
Only 3% of all of that waste is actually long-lived and highly radioactive, potentially requiring isolation from the environment. In France, this number goes down to 0.2% due to fuel being reprocessed.
Taking that into consideration, that means it would take about 2/3 of a century for the US to produce enough dangerous nuclear waste to fill this pool completely. And it can still be way more efficient.
Nuclear produces negligible amounts of actual waste for the amount of energy it gives us. The problems with nuclear aren't at all the waste, rather it's the current highly used methods that are used to harvest the fuel (slave labour and unsafe, dirty, destructive drilling). Very similar problems faced with, say, lithium and cobalt.