Seriously?

Your "simply facts" are partly wrong, and partly a half century out of date. It's a common problem. For some reason everyone presents stats on 1950s era reactors and then claims that those same stats should apply to reactors built today. Yup. How true. In fact, the computer I'm typing this message on takes up an entire city block. It was true in the 50s, so it must be true today! ;). Humans make the weirdest associations in their minds between facts that shouldn't be related, and it's hard to convince them that the faulty assumptions that come out of those mis-associations are incorrect.

1) Nuclear waste is comprised of a variety of materials, all of which decay to normal background radiation levels at a different rate, but none of which take billions of years. If something takes billions of years to decay to a non-radioactive state is isn't called 'waste'. We have a different word for such things: 'rocks'. The speed at which a radioactive material decays determines how dangerous it is. The faster it decays, the more radiation it puts out in a short period of time, and the more dangerous it is. If something takes billions of years to decay (like naturally occurring unprocessed U238), it isn't radioactive enough to be dangerous to a human.

The most dangerous waste lasts a few dozen years, while less dangerous waste (but still very dangerous) lasts a couple hundred. Neither of these are considered long term problems because they decay to non-dangerous levels quickly enough that the buildup of dangerous materials never becomes a storage issue (by the time new waste is created the old stuff is already harmless). The type of radioactive waste that is considered a problem is the stuff that lasts for a few thousand years. It takes long enough to decay and is produced in large enough quantities in currently active reactors that it is a PITA to store.

Newer reactors do not produce this long-lived waste in large quantities. Some designs create only a grapefruit sized amount of long-lived waste per year of operation. This amount of waste creation is insignificant on a per-watt basis, and can easily be safely stored for the thousands of years necessary. Note that storage itself isn't a problem. Storage isn't *that* expensive, and it isn't very hard. Finding geologically stable locations that won't be hit by natural disasters and aren't in someone's backyard, that's hard. That's why storage is an issue. Current reactors create long-lived waste fast enough that it cannot be stored at the available safe storage sites. Newer reactors create waste slower so that by the time a storage site is filled to capacity, the very first waste that was placed into the site will be ready to be removed (it will have decayed to the point where it is putting out levels of radiation similar to or lower than the background radiation that exists naturally).

2) All of the current generation of reactors were designed between 1950 and 1970. Saying "nuclear reactors are dangerous and create unmanageable waste, so we shouldn't build them" is like saying "Model T cars have a poor safety record, so no one should buy the 2011 model cars from Ford". That's just silly statement to make. Model T cars are dangerous, but they're also no longer in production. Those that still exist are relics of an earlier age. The same is true of nuclear reactors. Currently designed reactors are not only to all intents and purposes incapable of meltdowns (they are designed so that they passively shut down if the safety systems fail. No computer control or human interference necessary. They just... stop), but they produce far less waste per watt generated than the oldschool reactors that everyone uses as examples.

3) U235 is relatively rare in Earth's crust. However, unlike oil, which many countries currently import from volatile 3rd world countries, the vast majority of commercially recoverable U235 is in two 1st world countries: Australia and Canada. So unlike oil, energy security isn't a big deal with U235 based reactors.

4) U235 rarity is an issue. Most currently operating reactors (but not all) require a mixture of U238 (which is relatively common) and U235 (which is very rare and expensive to extract). MOST currently operating reactors. Most. Newer reactor designs are generally "breeder" reactors, which not only generate less waste than standard reactors, but they don't require rare resources to operate. U238 based breeder reactors have already been designed and tested — however the test reactors that have already been built (again, in the 70's) were too primitive to be economically viable, and research on them was cancelled for nearly three entire decades due to the low price of oil in most of the 1980s and 1990s. That was... unfortunate to say the least. (And the same unfortunativity applies to solar power research, geothermal research, and fusion research.)

While U238 is relatively plentiful source of fuel for newer generation fission reactors, research has also begun on a replacement reactor: Thorium based breeder reactors. Thorium is common enough to be a long term fuelsource, even if we were stupid and used *nothing* but nuclear power. (The best source of energy is a diversified source of energy. As many different types of power generation as is reasonable should be used in order to decrease the chances of a single bout of bad luck destroying civilization.)

5) Building power plants and mining fissionable materials are indeed fossil fuel heavy tasks. And so is creating solar panels. And so is making hydro plants. And so is making electric cars. And so is (to a lesser extent) building wind turbines. The reason behind this isn't because these activities *require* fossil fuels, it's because we just so happen to currently use oil and burn natural gas to accomplish pretty much everything we do. That's just the way our economy is set up. *Everything* requires large quantities of fossil fuels, because they are currently the energy source we use to do everything. That will change eventually.