California Institute of Technology - Caltech, Los Angeles
Hard to get into, but it has a really excellent reputation. Only 900 undergraduates, 1100 graduate students -- the only university I know of which has a larger graduate student program than undergraduate. We had a three hour orientation (my son got invited based on his math PSAT score), split into three one hour parts -- campus tour, Q&A with two current undergraduates, and an Admissions presentation on the school, tuition, scholarships, grants, work-study, etc.
900 undergraduates works out to an amazing 2 to 1 student to faculty ratio. We came away with the distinct impression that what they said about focusing on the students was really true. And every student has the chance to do real research as an undergraduate, often leading to publication. But, you have to love both math and science to cut it there.
The campus ground are quite nice, they reminded my wife and me of those at Rice Univ., our alma mater.
California Institute of Technology, or Caltech, is located in Pasadena just outside of Los Angeles. A small school with a small campus, Caltech is a big leader in research of science and technology. The school has a strong emphasis on the natural sciences and engineering. NASA's Jet Propulsion Laboratory managed by Caltech is also located in Pasadena. 30 Nobel prize winners come from Caltech. If you are a college student, it's not a bad idea to go visit the campus.