You’re right that most classes at Princeton will be fairly large, at least during the first year or two, when a student’s schedule includes a lot of intro classes. Where Princeton differs from some of the other highly ranked schools you’re considering is that Princeton requires a senior thesis (as well as junior-year independent work), and that the ratio of undergraduates to grad students is higher (because Princeton’s grad college is small). So at least in theory, you have more close contact with faculty. (Of course, YMMV, and certainly lots of students at peer universities get the opportunity to work closely with their professors…)