Sadly we're coming up on 3 years since we've last been down. But we've arrived late (or I suppose really early!) as well and then had a flight the next morning. Staying at the hotel is the way to go. We once roughed it and just waiting because we thought getting a room for 3-4 hours was a waste. It wouldn't have been.

As far as food, there's a restaurant in the Jetblue terminal that we always found to be decent. Haven't been to margaritaville there since we last flew American which was a long time ago.