It’s already on your list, but I just want to second Wisconsin as a great fit for you. Definitely a big-school culture, lively campus, beautiful setting (both the city and its natural setting amid Madison’s lakes), and a great place to study poli sci, with excellent academics and lots of opportunities afforded by living in the state capital. Along those lines, you might also consider the University of Minnesota and the University of Denver (where merit money could get you under budget, but I’m not sure).
As to Tulane, yes, it has a lower admit rate, but it’s much higher for men than for women (this is one of those schools that seeks to correct a lopsided male/female ratio).