Johnny Canoe is good but kind of expensive. The same people operate Conch Fritters across from the Hilton. Very similar food at lower prices. Unfortunately, it seemed to close on March 22nd and had not opened by the time we left on the 27th. It might be open again.
Next to Conch Chowder is the Imperial. It's mostly a takeout place but has some booths. They're open all hours (well, 23 hours).
Cafe Skans a block from the straw market has a very nice breakfast and snappy service. This is a real rarity on New Providence. Usually that's not an issue for us, but when we need to finish breakfast on a schedule to make our dive pickup, it is.
Traveller's Rest toward the western end of the island is quiet and across the street from a nice little beach. We had some of the best cracked conch of our stay there and the view could not be beat. Their conch fritters were especially chonchy, and they purport to be the inventors of the banana daiquiri.
Most meals we took at Arawak Cay at the "fish fry." There are a couple dozen restaurants ranging from hole-in-the-wall to two-storey places that take credit cards. Most have similar menus, but a few specialize or have very limited offerings (such as conch salad or scorched conch). We particularly liked Red Snapper, Twin Brothers, and Big 10's. Food here is uniformly fresh and good, and about half the price of Johnny Canoe. Some places offer breakfast, such as the stew fish and grits (and Guinness with carrot juice) at Red Snapper.
You can get to the fish fry on the number 10 bus (heading east toward town from the Wyndham) for a buck, and can get to Traveller's on the same bus heading west. If you hop on a bus and tell the driver you want to go to a grocery store, he'll get you to one.
and I would love to hear some of your recommendations on restaurants. 
