When I talk about this with my Dad, his concern is always that nuclear waste is horrible-awful-terrible and lasts basically forever. How is that stuff actually being stored, and how dangerous is it?
As a young lad, in the early '80s, my parents took me along to a "No Nukes" rally. It's not really a major issue for them, but they (or at least Dad) have been consistently opposed to it.
If you reprocess, the following things happen:
1. There is 30-100x LESS waste
2. You need 30-100x less uranium or thorium (in a normal reactor, for every 3kg of U-235 put in, there is 1-2kg of U-235 and 0.5-1kg of plutonium left at the end of the cycle..,which we store as WASTE!
We don't reprocess, thus we have a waste problem.
France has nearly the same number of reactors, and ALL their waste fits in a relatively small, and heavily shielded facility.
We (carter) made the decision to "set an example for the world and curb nuclear proliferation" by not reprocessing (since reprocessing is how you get plutonium...bear in mind, normal nuclear reactor power plant fuel cycles can't make bomb grade plutonium, only reactor grade mixed oxide fuel.
Since then, everyone reprocesses but us, no one else has a waste problem, and at least 4 more countries joined the nuclear club...smart guy, that mr. Peanut.
Also, you can use a concept like LIFE (laser initiated fission/fusion energy) or accelerator transmutation of waste (ATW) to take what waste you do have left and treat it.
Basically, the fission products come in three groups
Short and hot (10s-100s of year half life)
Annoying and hot (1000s-10000s year half life)
Long and cold (million year half lives)
Remember, the shorter the half life, the more radioactive a given amount of stuff is.
Category 1 (short and hot) is no big deal, you vitrify it, and store it in a building for 100-200yrs and it's gone.
Category 3 (long and cold) is no big deal, you dilute it sufficiently with dirt and bury it back in the ground...it's about as radioactive as uranium ore.
Category 2 is the annoying stuff, but it's a small quantity relative to the others. That stuff you blast with a neutron source and turn it into category 1 or 2. This takes power (about 10-20% of what the original reactor produced, or basically you need 11 where you used to need 10), but blammo, no waste problem.
With the above strategy, we have enough uranium ALREADY MINED to last hundreds of years, and no waste problem.