Volunteer your time for your city. If you have to choose between the basketball team and community volunteer work, choose public service. Brown University places a lot of emphasis in this area.
Write your admission essay and stress what makes you different from everyone else. Brown University loves people who stick out from the crowd and make themselves unique. In fact, a "go with the flow" type of person with a 4.0 GPA will be rejected before a unique 3.6 student.
Look at your GPA compared to your SAT score. Are they both high, or is 1 significantly lower than the other. If they don't match, you'll have some explaining to do during your Brown University interview. If your GPA is lower, it shows you haven't put in enough scholastic effort. If your SAT score is lower than your GPA, it might make them think your school offered easy classes.
Prepare yourself with specific questions about Brown University during your interview. Just like a job interview, you want to know a bit about the school and showcase your knowledge to the interviewer. If you ask specific questions it shows your enthusiasm (what Brown looks for primarily).