A question one can ask is why don't we build the reactors where we intend to store the radioactive waste long-term, a mile or two beneath the surface, at least half a mile below groundwater deposits. Such repositories already have to be accounted for the total price of nuclear energy, so why not build them there in the first place.
How the heck are you going to cool and service a reactor miles underground?? There's a good reason most/all reactors are next to a large body of water.
Cooling is an interesting question, because thermal-induced vertical flows in water are pretty strong and effective, and cool water is a lot heavier than hot water. You'd probably use large vertical tubes to surface, which would also mean quite high water pressure at the reactor, unless intermediate pumping stations and water reservoirs would be used –– which in turn could be used for kinetic and thermal energy storage from solar and wind power too.
As to maintenance: The same way you maintain a mine, or service anything related to large city infrastructure. At least here, they tend to be underground already. (In central Helsinki, about 100m underneath the Esplanadi park, there is a 8m wide, 40m tall, 80m long artificial "lake" with 25,000 cubic meters of water solely for district cooling.)
There is some extra cost involved in transporting stuff, as you use long spiraling ramps, not elevators, so it's comparable to having it say 30 miles outside your major city.
It really is much less crazy than might appear at first, especially for experienced civil engineers.