College of Wooster - specializes in 'average' students who didn't do exceptionally well in high school (but not poorly) and not for a lack of intelligence but a lack of a stimulating environment. The campus itself is very diverse, with multiple income levels heavily represented as well as the student body. This year alone had students coming from Bangladesh, Brazil, China, Ethiopia, Germany, Ghana, Greece, India, Jamaica, Japan, Kenya, Myanmar, Nepal, Netherlands, Norway, Pakistan, Paraguay, Romania, Russia, South Africa, South Korea, Tanzania, United Kingdom, and Zimbabwe. The town itself is in Ohio -- so in that sense it's maybe not as diverse as you're looking for.
Fantastic school with an active theater program and arts department. Oh and the band includes Bagpipes and the entire band wears kilts

As well as a state of the art psychology building -- including Monkeys that psych students can work with. They aren't used for medical testing but for psych testing such as left and right handedness. It is (technically) Presbyterian and there is a chapel on campus, but you wouldn't know it if it were not listed on college board.com and all other religions are equally represented with everyone being very low-key and tolerant. They are very generous with financial aid, and you would be eligible for merit scholarships. It's a personal experience, for instance, on your acceptance letter you get a handwritten note about your application essay, written by the President of the school. This school is great, and has repeatedly been called, including in the book Colleges Change Lives, "the best kept secret in education."
I went there for 3 years before transferring for reasons unrelated to the quality of the school, and my roommate was a Psych major.