Best BBQ southern Texas
Since that is such a short trip, there aren't many places off the highway (IH 37)...if your willing to take a side route, you may go 181 to Pleasanton, tx and have some McBee's BBQ. I like McBee's, they have good varity of meats...they even have bbq fajitas, and lots of sides...I usually pick up meats by the pound and some sides to have latter in Corpus.
I also get chicken and suasage at Van's in Oakview(37 south 1/2 way to Alice)...but I take a loaf of Buttercrust Texas toast bread and stop at the Rest area south of oakview and enjoy lunch under big Live Oaks. Sliced brisket on thick sliced white bread with pickle and onion...