As someone degreed in Physics, I have far less fear of the long term consequences of nuclear power and nuclear waste than many of the other byproducts of western civilization.
Also, as you point out, nuclear waste is very easily stored and contained which is what has always been done.
First, let it cool off for a while. We're doing this. Since the volume of the waste is so small, and it's so well contained, there's really no rush to process it right away.
Second, chemically separate it into its parts. Deal with them in different ways:
Uranium and plutonium can be recycled and used as fuel again. Hooray for recycling! France does this; other countries are just storing the waste for later, since non-recycled uranium is cheap these days.
Short-lived isotopes can be left to decay. They are short-lived, after all. This is happening as we speak.
Medium-lived isotopes are the really troublesome ones. Hit them with some spare neutrons to transmute them into something shorter-lived.
Put the remaining, much-diminished waste in storage. It should become harmless after a few hundred years, rather than a few hundred thousand.
Fun fact: it's a lot easier with something like a liquid fluoride thorium reactor, which makes the chemistry really easy and prevents a lot of the nasty isotopes from forming in the first place. You can skip most of the rigmarole.
(Huh. I guess that was longer than I thought. Oh well; who needs sleep, anyway?)
President Carter banned reprocessing in the US over bogus weapons proliferation concerns; IMO, one of the worst things a President has done in the past 60 years.
I am a bit torn between "just build a lot of 3rd generation reactors" vs. going for the fourth gen designs.
In addition to pjscott's comments, I'd add that I believe that the risk's associated with radiation and radioactive waste are relatively well understood compared to the risks associated with manufactured chemicals and pharmaceuticals (for example). In these area's, we have a tendency to perform a trivial study of the toxic effects of a compound, release it for general world wide consumption, then decades later figure out the biological and environmental consequences.
Another byproduct of western civilization are our various systems for governing nation states. Those systems, in the 20th century alone, caused somewhere between 100 million and 200 million deaths (largely from war, famine and 'democide' initiated by governments, politicians & dictators).
I fear chemical compounds whose names I can't pronounce and governments who murder their citizens far more than radiation.