If it were not for the political problems, it wouldn't be that hard. Pick some hard-rock mountain in an unpopulated geologically stable area that hasn't changed much in the last 20 million years or so. North and South Dakota have mountains like that. Drill tunnels, well above the water table. Encapsulate high level nuclear waste in glass and put that in big stainless steel thimbles. Lower those into holes in the tunnels.
France does something like this.