Here is a link to information on the Traveling Wave Reactors (Terrapower) referred to by Bill Gates that burn nuclear waste as fuel and runs for 50 to 100 years without refueling.
You end up with a much smaller volume of nuclear waste. For at least 50 years, there would not be any waste to store. Traveling Wave Reactor waste:
"If you received 100% of your electricity from nuclear power for your entire lifetime, all of the nuclear waste generated from your use would fit in a coffee cup." Nathan Myhrvold is a founder of the company that owns the Terrapower design. He used to be the chief technology officer at Microsoft.