Gravity, mechanical and chemical energy storage doesn't really come close to what's needed.
Wind and solar have intermittency problems, of course. Nuclear has waste problems and is best at supplying a constant power, but of course the load varies.
The solution is simple. Enough small fission reactors to cover peak demand, but these should be designed to be /reversible/. Enough wind and solar to match the average demand. When demand is off peak, some of the nukes will take power to convert their waste back to fuel. When the wind is up and the sun has got its hat on, more of the nukes will run in reverse.
At a stroke, no more waste accumulation and enough power for all.
I'll let someone more qualified do the reactor design, I have Middle East peace problems to sort out now.