Like Rhone Man, I go to Lone Star to drink beer and watch a game on TV (and I sit in with the band occasionally), but I'm not sure I'd make it a point to head there for the food - although it's not bad. If you go to Seven Mile Beach (and it's only a 10-15 min drive from the airport) there are lots of better places for food and/or drink.
Working from a weak memory here, but going south to north you have the Wharf ($$$), Fidel Murphy's (good beer), XQs (kind of a sports bar), Coconut Joe's, Pepper's (great steamed island style fish), Chicken! Chicken! (great jerked chicken), Lauren's (good all around less expensive casual), Decker's (a bit more upscale), Hemingway's ($$$ but on the beach), Sunshine Grill (seems to be the all time favorite around here - we go there a lot), and Eats (like Lauren's) - and that's probably about a far north as you might go. Although if you take the Tibbetts Highway up the middle of the island to the north end of the beach you can get there quickly - and either grab an upscale meal and drink at the Kimpton beach bar or circle back on the shore road and hit either Duke's (good food, casual, reasonable prices) or you can hit Calico Jack's beach bar and just drink along with the locals, and maybe after a few you'll decide to ditch your flight and just stay.
