Plenty of decent places (Señor Frogs, Athena, etc) in Nassau that are in walking distance, though not sure I would recommend them over places that are a short taxi ride away. What kind of food are you looking for? One common theme in Nassau expensive food for what you get.
Other can add, but some ideas:
Ichiban, decent Japanese place around then corner heading away from town.
Graycliff, more formal and expensive. Walkable.
The Poop Deck-taxi ride away, informal, on the H20, good grilled seafood
Matisse-nice place. Walkable. Good food.
Luciano's. Taxi ride. Good Italian, nice atmosphere.