Welcome fellow AA PLT NYCer. Do you have any limitations fare wise, are you looking simply to gain miles or get best miles for the money. If the former, I think there is a late night flight to LHR that you could take Sat PM and then return MON PM (and use the club at LHR to shower and change-I fairly certain that the club at LHR has a shower, but check). Or even possibly the late night JFK flight to EZE (Buenos Aires) and 3/11 PM. If this is out of your fare range might check for flights from LGA to SAN (running around $250 or so with taxes) connecting through ORD and/or DFW.