+1 for Dive Provo, Provo Turtle Divers, or Big Blue. If the weather is calm enough they will take you out to West Caicos or French Cay which both have some great sites but do require about an hour of travel time each way. Otherwise you will end up diving in Grace Bay which is just ok (but very close).
If you're really feeling adventurous for a few days, take the short flight over to Grand Turk (airfare from $45 each way) and spend a few days diving there. The hotels are significantly cheaper and the diving is much better. Many more sharks, turtles, and eagle rays and the wall structure along the Turk Passage is fantastic.
When it comes to food on Provo, most of the places for a good (cheap) bite get overlooked. Many of the places that have been suggested so far are excellent for a very nice, expensive, sit down dinner. If you can afford to do that every meal, go for it since most of the hotel restaurants do serve excellent food! But if not... Within Grace Bay (and an easy walk from most hotels), Jimmy's Dive Bar does descent food (and their happy hour drink prices are very acceptable for what you get). Right down the street from Dive Provo is an upscale grocery store called Graceway Gourmet that actually serves good lunch fare from their deli. Across the street from the grocery store is a small collection of buildings that sell shells/trinkets and one of them is called the Pork Shack which does great Jamaican BBQ type sandwiches. If you have access to a car, Rickie's Flamingo Cafe is a little past Club Med and does excellent food for a reasonable price (and is probably the best location to watch the sunset!)
Every Thursday night, the island also does a "Fish Fry" in the park on the western end of Grace Bay. There is always good music and lots of local food vendors (where you will find some of the best fish and jerk chicken/pork). It is always popular with locals (especially ex-pats) and the tourists that know about it.
If you are looking to do something that doesn't involve diving for a day, take the ferry over to North Caicos and rent a car to drive around North and Middle Caicos for the day. The caves on Middle Caicos are very cool and those two islands have some of best natural beaches in the world. Mudjin Harbour in particular is frequently rated as the most beautiful beach and there is now a nice little restaurant overlooking it where you can get good food. It's very easy to not get lost driving around the two islands since there is really only one main road that goes straight through both of them. You can then take the ferry back over to Provo in the afternoon. The ferry ride is like 20 minutes each way and drives you through all of these gorgeous little cays on the way. It's a great day trip!
I'm happy to provide further suggestions if there is a type of food in particular or something you are considering doing, just send me a message! I have been living in the Turks and Caicos full time
