I was born and raised on the Gulf Coast and there are many hunting opportunities, it really depends on what you got you heart set on, Duck hunting, hog hunting, deer hunting, Geese Hunting, and what price range you are willing to pay?  If it were me, i would do a cast and blast (ducks and reds / trout) either in Rockport or further down south in the Laguna Madre.  But I would not count out researching some great deer or hog hunts on the Guld Coast that can be very special, the South Texas brush is just amazing on some of the coastal areas.  And if you don't have any success in the field with a riffle, get out the old fishing pole and try your luck at some fine saltwater species, winter time there can be some great fishing to be had!!!