Mobile is all about seafood. I really like Wintzell's Oyster House. There are also several places on the causeway out past the battleship exhibit, but they can get crowded.
Touring the USS Alabama is a quick and inexpensive trip. You can also get a sense of the claustrophobia of serving aboard a WW2 diesel submarine (The USS Drum), which is out of the water and next to the battleship. There is a seafood place next to the battleship park (Captain's Table). It is not very good.
I think you will like the port of Mobile. Very professional and friendly staff and an easy port to use.