AAU = Amateur Athletic Union. It's a league for typically school aged kids, but not affiliated with a school or a church (often schools have teams as well, there is also "CYO" (Catholic Youth Organization) which sponsors leagues, and many Jewish community centers and YMCA's also sponsor teams/leagues).
Check http://www.aauboysbasketball.org/ for boys and http://www.aaugirlsbasketball.org/ for girls. You should be able to find local teams in your area if you look there.
AAU is a very competitive league, in general, so I would not be at all surprised to find college scouts at games.
Good luck!