The battleship park is interesting. They have several military airplanes too, as well as the submarine - definitely a claustrophobic experience.
Lots of seafood of course. Wintzell's Oyster House
is famous. They've started franchising but this is the original location.
There are also several restaurants along Battleship Parkway (highway 90) which runs across Mobile Bay. Be aware the police love to sit all over this road and run radar.
Speaking of restaurants - right at the entrance to the battleship park is a place called The Captain's Table. Don't go there. Expensive, poor service, and the food is inconsistent.