Cheap is the Big Fisherman in Rockport but I will not go back. I have not found a place on the Island that I really like. I do hit Corey's seafood on 361 in Aransas Pass across the street from the HEB. Have fun and do not forget the fishing pole.
I used to like the Big Fisherman when I ate fried food regularly. If you are into that kind of thing, then it is great, if not, don't waste your time. We like going to Trout Street, Beulah's is good, Seafood and Spaghetti Works has great seafood (the dome looking building), like driving into Corpus and going to Snoopy's and Scoopy's. Also, if you are going to be there a while, it is a nice drive down to King's Inn.