When I was in Corpus Christi, my favorite spot to eat was Taqueria Jalisco. Great food. They are a mom and pop chain that stayed local to South Texas.
The beach is pretty cool along along South Padre Island. Lots of tiny deer along the beach once you get out of town.
I wouldn't recommend swimming so much in remote areas; I used to fly over that part of the country in SAR helos...lots of tiger sharks.
Corpus used to have a lot of strip clubs along South Padre Island Drive.
Some great water side seafood restraunts on the outskirts of Corpus Christi.
Take a fishing charter if you have the time. Rockfish and sea trout (red trout?) fishing is pretty good even in the knee deep water.