On the causeway:
Felix's - probably the best all-around food on the causeway, run by same people that run Ruth's Chris steak houses.
R&R Seafood - Good steamed crab and crawfish
Oyster House - Great salad bar and grilled oysters. Good seafood. Great deserts. It's a bit of a tourist spot now. Local knowledge: there is a baby gator living in the marsh at the dock behind the restaurant. We have to go try and find it every time we eat there (I have a 6 year old).Blue Gill - Usually have good music. I think the food is not as great. YMMV
Tacky Jack's - OK Seafood. Never been too overwhelmed by it, but some people really like it.
Lap's Grocery & Grill - Huge place with very few tables, strangely. They have multiple bar areas. They have pretty good food here. Live gators at the bottom of the back stairs, so if you have kids they may like that.
Ed's Seafood Shed - Seafood, decent but not as good as other spots. Has the best views of any of the places on the causeway (except maybe Felix's, but Felix only has inside seating) and it has a great outside deck over the water. Decent music some nights. Good cheese grits.
Eastern Shore:
Bass Pro Shop - Meh. It's a chain seafood restaurant. It's average at best.
Tropics - Haven't tried it yet. At the very end of the causeway on the eastern side. Lots of beach volleyball courts.
Big Daddy's Grill - Good seafood. Off the beaten path, but really cool fish-camp feel right on a river with boats docking, marina, etc. Use google maps to find it.
Old 27 Grill - Also off the beaten path. Good burgers, southern american food. Nice music some times. Outside eating mostly. Use google maps to find it.
**** tons of chain restaurants right in Daphne at the first exit.
Fairhope has a few nice restaurants but I haven't been over in so long that I can't really tell you much about them. I can tell you that Old Bay Steamer is no longer in business.
Mobile - downtown:
There are tons of places so I'll just list the ones that I have experience with that I'd also recommend. There are certainly others though.
Callaghan's Irish Pub - GREAT burgers, it's a straight-up irish dive with good food. It's relatively close to the stadium in the middle of an old neighborhood.
La Pizzeria - Was closed for a while, now reopened. Good italian dishes and pizzas. Near the stadium also.
Kitchen on George - Great nicer sit-down place to eat. Has the feel of an upscale city place. Great food and it's a part of the culinary school here, so the waiters, cooks, etc. are all part of that program, I think. Really good food. It has a small bar too. We've taken our kid once but it isn't really a kid-friendly menu.
NoJa - On North Jackson street (get it? yeah, catchy). Good higher end food in a nice atmosphere. Not really a kids place.
Spot of Tea - The owners are MSU-friendly (though not MSU grads). It's where we have most of the alumni functions in town. Decent souther american and "pub" food and you can sit in the park across the street and they'll bring your food over to the tables.
Bikeshop - is supposed to be good but I haven't been.
Wintzel's - is on every eatery list but to be truthful, I hate the food there. It just tastes like run of the mill old seafood joint to me. Maybe their oysters are to die for and that's the reason everybody puts them on a list. I don't really like raw oysters so I just don't know. It's been on various Food Network shows.
We don't spend tons of time downtown so I'm sure I'm missing a BUNCH here.
Mobile - other:
Via Emilia - One of the best places for really good food in Mobile, in my opinion. They have a chalkboard menu so it changes a lot. The filet is always on the menu as far as I can tell...and for good reason. It really is that good and I'm a food snob.
Easy to find. It's right across the street from USA's basketball arena.
Jerusalem Cafe - Nice quality mediterranean food. Small place. In a strip mall behind Applebee's on Airport.
Brick Pit - Really good BBQ. MUCH better than Dreamland (though I like DL's sauce). Brick Pit's smoke flavor in the pulled pork is really top notch. It's been on various Food Network shows. About a block from USA's campus on Old Shell. It's in an old house, as all good BBQ places should be.
Hungry Owl - Good food, it's also been on a couple of Food Network shows for some insane hamburger that they have there. Waaay out west on Cottage Hill Rd. just past Shillinger Rd.
Every chain restaurant that you can imagine is probably on Airport Road somewhere: Chipotle, Jason's, Moe's, Bonefish, Macaroni Grill, etc., etc.
There are so many places that I'm sure I'm missing a few here also.