I would suggest the Lobby of the Airport Hotel (there are some couches there) at Terminal E (near your Customs exit, but on the departures floor)
I would second that idea.
MIA has a decent amount of shops and resturants before security if you get bored or hungry. Also you could always walk around and just keep an eye out on the arrival screens and you can meet them right there at the exit for international arrivals. All Internatioanl arrival passengers for that terminal BA and AA terminal, come out from the same little spot.