Like people say, you can check in at anyt. IMHO, it's best to check in at the terminal and ticket counter closest to your departure gate. Call AA before you go to the aiport to find out which terminal andgateit leaves from.
Some cities always, or are at least supposed to, fly to and from the same terminal. LAX is one of these cities (it is a B terminal city), although on Thursday we arrived at C. Very, very unusual.