Tortuga's and Black Marlin, two of the best in Port A, can both be booked via OpenTable. Both are excellent, but you need to be on time or they will cancel your reservation. If you go to Tortuga's, don't fall for the South American fish. Eat the local and fresh seafood. Their seafood fondue (or something like that) is a great starter. On my last visit to Black Marlin, I was served perfectly blackened redfish. It was perfect! At both, the grit cakes are fantastic. If they don't come with your meal, order a side.
Phoenix is great. Fantastic food. You can call and get reservations. I've only eaten outside and never seen the interior.
Venetian is good Italian. Like mentioned you will need reservations to get in.
Roosevelt's is more of a special occasion restaurant. If you want to dress up, this is the place for you. The 1886 bar next door is a good place to start or finish.
MacDaddy's is good and has a wide selection. I know they have BBQ, which is surprisingly good, and plenty of other classics. It's simple food for the most part but excellent.
Blue Water Cowboy is nice with a small menu. It's a good balance between a place where you want to eat AND drink as it has a nice neon vibe to it. Interior is nice. It might be owned by an Aggie based on the decor.
Crazy Cajun is a classic if you want boiled food. Think shrimp, crawfish, potatoes, corn, etc.
LaPlaya is above average with a more diverse menu than TexMex restaurants and is usually crowded.
If you want to sit by the water, Fin's and Grumbles are decent. You'll need to request a view of the water if you want it at Fin's. Fin's is sit-down service. Grumbles is counter service with a full bar. You get to choose your own table.
Virginia's? On the water? Yep. Will you get a view? Who knows. Food any good? Nope.
Stingray's is a good place to watch a ball game. I'd recommend simple foods and drinks. The rum bucket will take you out.
Irie's is casual and good for fried Gulf Coast seafood. They use a heavy, probably Panko, batter. Fried shrimp and fish is always a good choice. PoBoy is decent, but a far cry from anything in New Orleans.
Kody's? Love them for some reason. The interior is a dump, but the food is on par with Irie's. Good food, but some of the selections are highly priced as specials. Stick to the Gulf Coast classics.
Spaghetti and Seafood Works is good and has a good mix of seafood and pasta dishes. It's nice inside.
Swing bar is nice if it's not too crowded.
The Gaff is a dive bar serving beer and wine -- no full bar. It's a a classic though. Belt sanding races on select Saturdays. If you're wearing something nicer than blue jeans and a t-shirt, you'll definitely stand out.
Try Coach's for breakfast if they've made it back up on Allister Street. The breakfast taco is fantastic, and the pancakes are huge and require little to no syrup due to their sweetness.
I hope you enjoy your time there!