There is the Starry range on yorktown just before you cross into the bluff to the right, its $10 a gun a day.
If you plan on being in Corpus for any amount of time you can get a membership at the Corpus Christi Pistol and Rifle Club, for $125 a year you and your family/friends can shoot as much as you want. They have a pistol range as well as a rifle range to 500 yards, although I heard they shut down the 300 and 500 because a subdivision is going in behind the place.
They also have a tactical range, sillouette, and trap and skeet that costs extra.