The world needs a new source of energy, an unspillable source.

If we decide to increase our use of Nuclear energy, what do we do with the additional waste?

Nuclear energy already supplies 20 percent of our energy. If we were to build my plants, how would we handle the waste? After all, it does have a half-life of 10000 years.
Who would want it in their backyard? What place is safe from earthquakes, fires, hurricanes, and far from a population center?