While "colleges" might not have art museums, many of the large universities do. My school was University of Texas, Austin where there is a brand-new museum of art
as well as other museums on campus. The College of Art has its own museum where rotating exhibitions are mounted, including the student exhibits for both undergrad and grad students (MFA thesis show, for example).
An added bonus is the College of Art library which is as large if not larger than many big city public libraries - and it's devoted to art references of all types (visual, performing, and music).
Very wise to begin looking at this at your age. Best of luck to you!
Postscript: Are you currently attending school in New Mexico. If so, have you checked into UNM's MFA program for "Museum Studies?"