I'm studying baby Rudin before entering college as a math undergrad. I'm younger than the OP, but I find it to be stimulating. It's important that you try to prove theorems before going on to read Rudin's proof, and do the exercises at the end of each chapter so the concepts will cement...
To answer your question, I'm looking at UGA and UT. I have friends in both areas, and I love both locations. I currently live in Athens, so UGA would be nearby, but Austin is nice too.
I'm in home school. I haven't had much formal math instruction.
I plan to go the path of mathematics in college. I've always been an adept at solving problems and writing proofs.
I'm only 17 and doing self-study. I checked out from the university library the second volume of Calculus by Apostol and Principles of Mathematical Analysis by Rudin. These should...