I am not sure if there is a Baffin Bay in Texas,unless it's named for the one in Canada. You might Google them,I think they have a website.
There is also Snoopy's in Corpus Christi,near one of the bridges, they too have a website as does Clear Springs Catfish in Clear Springs,Texas near New Braunfels on Tx.Hwy 46.
Despite the influence of the Spanish and the Catholic Church here, there really doesn't seem to be much in the way of seafood here at all. Louisiana yes,and up north like in Wisconsin,etc. I think it's because of the culture you have here. I think most seafood dishes even in Mexico are coastal ones,found mainly on the coast rather than inland. In Louisiana you have mainly french, and even germans and some hungarians among other groups.
Us Catholics in the old days couldn't eat meat on Fridays because that was a day of abstaining from meat,because Jesus died on Good Friday.
Even years ago my dad said it was strange that San Antonio, which is only 300 miles or so from the coast was lacking in seafood places.Heck,Port Lavaca is only 90 or so miles from here if you go out US Hwy87.If there are any good seafood places here in Texas, they don't advertise much.