"Good" private schools (Harvard, Stanford, MIT etc.) charge a lot for tuition then redistribute funds so that people from less affluent backgrounds get need-based scholarships. I think this pressures other private schools to raise costs in order to seem competitive, even though they don't often have the same generous financial aid. In some cases, going to Stanford may be more affordable than going to Berkeley even if you're in-state.

The strange consequence of this is that it is almost better (from a selfish viewpoint), if you are not rich, to not have money saved for college if you send your kid to Harvard, because they'll take any money you do have.

The room and board cost is mostly based on cost of living (Boston and the Bay area are more expensive than Madison, Wisconsin), but financial aid will often cover that too.