What are good colleges to apply to if I want to become a stock broker?

First you should think about what majors are good if you want to be a stock broker. Finance is definitely a good major for being a stock broker, and since you already asked a question about college that are good for finance, that's a great start.

Other majors that are helpful include Accounting, Economics, Statistics, or Math. Colleges that are the best for those majors are as follows, all according to US News and World Report unless otherwise noted.

Accounting

1. University of Texas - Austin
2. University of Illinois - Urbana - Champaign
3. Brigham Young Univeristy - Provo

Economics (from Education Portal)

1. Harvard University
2. University of Chicago
3. University of Minnesota - Twin Cities

Math (from College Confidential)

1. MIT
2. Princeton
3. Harvard

Statistics

1. Stanford University and University of California Berkeley tied for first
2. University of North Carolina at Chapel Hill
3. Harvard University
4. Iowa State University

Also see the answers to the question "What colleges should I attend to get a business degree?"