I wanted to put in a plug for Rice – it has small class sizes, beautiful green campus in an urban area, sports, no Greek life but a residential college experience that is fantastic, and an amazing music school. There are several a cappella groups and an orchestra for non-music majors to join. (My daughter sings with the Rice Chorale, which is for both music and non-music majors – and the director often pulls in accomplished instrumentalists to accompany them.)
The graduate business school is established and respected, although the undergraduate business degree is relatively new. However, they also offer economics, managerial economics, mathematical economic analysis, financial computation and modeling – all as majors. There’s an entrepreneurship minor, too. I don’t know anything about investment banking, but one of these might work for you.
It’s a strong STEM-focused school. And despite its stellar academic reputation, it’s a quirky place that’s friendly and not competitive. Students score internships readily. My daughter is having an amazing experience, but she chose it mostly for fit. (There were certainly cheaper and more practical options, lol.)
The cost will be the biggest sticking point. Rice offers really good need-based aid, but the merit scholarships are hard to get. Cost is $75K+ a year.