If you are coming in on an AA flight I would suggest hanging out in the Flagship Lounge in T4 for a while. The wifi actually works pretty well there and you can actually see outside. There is an airside shuttle that runs from T4 to TBIT. It can be kind of fun to race a 747 or a 777
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When I did this at the end of May the Flagship Lounge wasn't too crowded and the food choices were ok.
Enjoy your trip!