Could we Nuke our garbage?

You don't need to nuke it...some companies like CWT already use a process called thermal depolymerization to break down and convert organic materials/garbage into oil or fuels. Plastics as well can be converted back into oil through various methods. Or plasma gasification processes can be used. All sorts of ways to convert garbage and even highly toxic materials into fuels or disposed of safely. With the millions of tons of garbage we create in the world every year, much of it could be converted into fuels via various processes.

https://en.wikipedia.org/wiki/Thermal_depolymerization

https://www.youtube.com/watch?v=7-0o3rgoplw

http://discovermagazine.com/2003/may/featoil

https://www.google.com/search?rlz=1C1AOHY_enUS819US819&biw=800&bih=487&ei=ORwfXZ2TBMfOtQbetY7YBg&q=garbage+into+oil+&oq=garbage+into+oil+&gs_l=psy-ab.3..0i22i30.3926.9385..9541...0.0..0.258.3411.2j15j5......0....1..gws-wiz.....0..0i71j0i67j0j0i131j0i10.vb3XpE2bamg

at $10,000 a pound, that makes a lot of sense.

We want as few of those things going off anywhere on the planet as possible.

Throw it into Volcanos

no, that would be really expensive and harmful to the environment

Don't hold your breath waiting for a phone call from Stockholm.