Actual nuclear waste is a 10,000+ year problem, not hundreds of years. But the 100s of years problem is more about where long-term storage should be (Yucca Mtn. etc.).
When you tour Hanford, what do you see (free tours for US citizens, BTW)? You see many ancient reactors - all disabled now except the preserved first reactor. You see -every single decommissioned nuclear submarine-'s reactor in long lines. And they remind you: based on ice ages, in 15,000 years or so, it won't matter... the entire plateau around Hanford will be under water. So it's going to need to be somewhere else.
Wild stuff.