Food is a little more expensive here than on the mainland.
The food shacks that line the road to the port all cook up similar fare: parothas Tk 8, omelettes egg, Tk 20 and vegetable curry Tk 20 for breakfast, and fish, dal, rice and veggies at 130 Tk the rest of the day. Cha is Tk 8.
All of the hotels also have restaurants with basically the same typical Bangladeshi offerings, with higher prices and better quality than those near the port. Chicken is sometimes available but not very tasty, and lobster and crab may be available occasionally at very high prices. The restaurant at Blue Marine Resort and Appayan at Saint Martin's Resort are the best on the island.
The islanders also sell dried fish, which is a bit more expensive but fresher than those available upshore in Cox's Bazaar.
Early morning is the best time to get fresh fish from the fisherman near the market, you can often bring it to your hotel chef and ask him to fry it up the way you like, or some places may do a nice evening barbeque. Some places may even give you kitchen access to cook it yourself if you ask.