There are many excellent colleges that have a predominantly minority student population. 

Hispanic Association of Colleges and Universities

Historically Black Colleges/Universities
     (by region and state)

Tribal College Listing
     American Indian Higher Education Consortium 
     (includes articles of interest to prospective students)

National Consortium for Graduate Degrees for Minorities in Engineering and Science, Inc.
     Contact list for schools with a minority program

See also:
Preparing for Graduate Work