The Aransas National Wildlife Refuge is a wonderful birding area. It is the winter home of Whooping Cranes along with numerous other birds. There are trails, observation towers, and boat tours available. http://www.fws.gov/southwest/refuges/texas/aransas/
Our favorite park in this area is Pioneer Beach Resort in Port Aransas. It also has a pond area that is supposed to attract birds, and the town of Port Aransas has a nice pier on a lake for watching local birds. Gulf Waters Beach Front RV Resort is supposed to be nice too, but we've never stayed there.
Also the Rio Grand Valley is an excellent birding area. We have not been there for over 25 years so I can't comment on places to stay, but there are bunches--well, there were bunches before Hurricane Dolly. I'm sure they will get cleaned up quickly though. South Padre Island KOA has gotten good reviews lately. Also look at the reviews under Brownsville, and it will list the names of other nearby cities.
Try this website for birding information. http://www.worldbirdingcenter.org/
Hope this helps.