If you want to go OW, how about AA to SJU ?
2.5 hours each way. If you want an overnight, I can't recommend the Club level at the Riz Carlton San Juan highly enough. A fabulous property which will beat hands down anything that the traditional Caribbean (inc BGI) has to offer ! Not to mention the Plaza de las Americas shopping mall, if you want serious some heavy duty US tax free shopping ....
Was there last week for a one night stand (so to speak !) en route to London and had a great time.