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There's a high-end steakhouse right in the AA Terminal at JFK.

In Forest Hills -- about a 20-minute cab ride from the airport -- you can find one of the best pizzerias in the city (Nick's), as well as another high-end steakhouse ("aged"), an Argetinean-style steakhouse (Pampas Aregentinas on Metropolitan Avenue), Italian (Family Restaurant, Portofino), Greek (Corfu, Agora), bistro/pub (Bonfire Grill), etc. There's also a very good kosher deli (Ben's Best) in Rego Park, which is a few minutes further away than Forest Hills.

You certainly have time to go into Manhattan for dinner if you want to, and could do the roundtrip for two for under $30 via AirTrain and the subway.

As to your baggage, won't you be checking it through to HKG when you check in for your flight at TPA? Or will you have carry-ons?