Also, as serfty mentioned, there are multiple AA lounges at some US airports, usually one per terminal in the larger hubs and none at all at some airports such as BWI. In general, the AA lounge that has the children's room, I find, is usually the largest and the best, this is true at DFW. I think that if you have over an hour to spend at such airports, look for the AA lounge that has the children's room, and use the skytrain for connection to your terminal if it is near the lounge with the children's room.
It will only add about 10 minutes extra to move from one terminal to another, I think that MIA is the same. The AA lounge at SFO is a lot smaller, and hence no children's room, the one at LAX is much larger (terminal 4) and has a children's room, seems to be the pattern, children's room = best AA lounge at the airport.