Probably one of the best sandwiches I've ever had would be the Schwarma special at Little Jerusalem in Simpson Bay and
I come from the land of great bread and the home of cheesesteaks.
Although not on inexpensive side, if you are going to splurge and try lobster thermidor, Pineapple Pete's is reasonably priced.
Captains D's roadside grill is great for take out.
Grab a pizza at the boatbar in Maho.