To the OP, I went to NESCAC for undergrad and Ivy for grad school. I'm happy with those choices. Painting with a broad brush, I think most that I know enjoyed their undergrad at NESCAC schools more than Ivy Leaguers enjoyed their time - the schools are smaller and more personal. The education is generally better. It's true than most Ivy's have better brand names, especially with the general public, but that doesn't matter much in the end.
Think a bit about what you may want to do - a few fields that care a lot about pedigree, notably management consulting at the brand name places - don't hire much from the NESCAC schools, other than Williams and Amherst (or at least they didn't, I may be dated). That could be true for investment banking at some NESCACs as well.
Think about the academics. Obviously, NESCAC schools for the most part don't have engineering or very deep science departments. You get more time with professors who care more, but there is less breadth and less depth - if you want to focus on string theory, for example, your NESCAC of choice may happen to have a string theorist, or it may not - but Princeton will have a whole sub-department.
If you are a true genius, you should probably go to a top Ivy or MIT/Caltech. You won't have many peers at the NESCAC, but you may at the Ivies, especially with their grad programs.
For the vast majority of fields, the degrees from top NESCACs will be equivalent to the Ivies. No med school, law school or grad program cares that you went to Swarthmore rather Harvard.
Finally, as noted above, there is a huge range in terms of prestige within those groupings. Harvard, Yale, Princeton, Stanford, MIT, Caltech are at the top of Ivy +. Columbia is a step down, and Penn, Brown and Dartmouth are another step down, with Cornell seen as being last.
For the masses, nothing will beat the name recognition of an Ivy. But among the well educated, I think most would place Amherst and Williams at the Penn / Brown / Dartmouth level or maybe with Columbia. Many would thrown Pomona and Swarthmore right there as well, or perhaps a bit lower, with Bowdoin, Middlebury and Cornell. It's a big step down after that to Bates, Colby, Conn, Hamilton, etc.
If you want to impress a date at a roadside bar in rural Kansas, Williams ain't gonna do it. But the vast majority of employers or schools will consider a degree from Williams and one from Columbia to be equivalent. And you'd probably enjoy your time at Williams more.