A typical nuclear power plant produces less than 30 tonnes of waste per year. Most of that is not really waste, though, as fuel reprocessing would allow more than 90% of that to be made into new fuel. Less than 4% of the spent fuel is actual waste (fission products) that have to be stored. If we were to reprocess fuel like the French and the Japanese, then a reactor would only produce about 2 tonnes of waste per year.
Spent fuel is not unusable because the fissionable fuel is used up. The reason spent fuel in its current state is unusable is because many of the fission products generated during normal operation are very good neutron absorbers ("poisons" if you want to use the industry lingo). If spent fuel were put back into the core, the operators would not be able to keep the reactor at power because the number of neutrons absorbed by these poisons would prevent enough fissions from occurring. Reprocessing allows for the separation of fission products and fissionable fuel. Once this is done, the fissionable fuel can be put back into the core. This process greatly reduces the quantity of waste (but not the radioactivity, as the fissionable Uranium that is removed is barely radioactive), and it also would allow much more energy to be extracted from a given amount of Uranium.
We don't reprocess for several reasons. Obviously, the politics are one reason. But the biggest reason is economics. Uranium is so abundant and so cheap right now, there is no reason to build a reprocessing plant when it would be cheaper to simply buy new fuel. Once the market changes, though, reprocessing can become more appealing. If and when this happens, spent fuel repositories will actually be used as sources of new fuel.
As for what to do with the fuel, we already have a solution. We can store waste in remote national repositories until it is advantageous to reprocess it. The problem is that certain groups like Greenpeace would rather exploit the problem than solve it. They don't want national repositories because they know that a solution to the waste problem will increase the popularity of nuclear power. It is tactics like this that have driven people like Patrick Moore (a co-founder of Greenpeace) out of that group and into environmental groups that support nuclear power.
The worst thing about this debate is that people look at nuclear power in isolation too much. Yes, waste is an issue, but it is less of an issue than it is with other sources of electricity. Nuclear power plants collect, catalog, and store all the waste they produce. Then we all bicker and argue over what to do with it. Coal and natural gas plants simply vent most of their waste into the atmosphere, dust their hands off, and say "see, we don't have a waste problem!"
The bottom line is that there are only three technologies are practical and available right now that can expand electricity production -- natural gas, coal, and nuclear power. Natural gas and coal spew toxic waste and greenhouse gases into our atmosphere, and that is when the plants are functioning exactly as they should. The US gets a little more than 50% of its electricity from coal, and those plants produce as much carbon dioxide and more toxic pollutants than all the cars in the US combined. These pollutants kill people and damage the environment every day. Nuclear plants seal up their waste so that it can be stored where it will cause the minimum harm to people and to the eco-system.
As for cost, nuclear power is competitive with natural gas in terms of cost per unit of power produced. That accounts for construction, operation, waste storage, and decommission (nuclear plants in the US pay a tax that goes towards waste storage and decommission). Since waste is controlled and stored, the cost for nuclear includes externalities. Coal and natural gas do not account for externalities when they calculate a cost per unit power. How much more do you think these power sources would cost if plants had to pay for people dying of lung cancer or suffering from asthma?
That is the case for nuclear power. Nobody knowledgeable claims it is perfect, but it is by far the best choice we have. Coal and natural gas (and oil where it is used for electricity) are literally killing us. Hydro is tapped out in most developed nations. Nuclear is statistically safer than all other major electricity sources (in terms of deaths per unit power produced). In light of this, the waste "problem" to which we already have viable solutions seems rather tiny.
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In the interest of full disclosure, I am a nuclear engineer who is employed by a nuclear vendor (a company that designs and supports nuclear plants). I am not speaking as a representative of my company, but rather as an individual with above average knowledge on the subject.
