There is nowhere to eat near the AT&T center unless you plan to eat at a run down Bar-b-que shack or inpromptu Taco Stand. Both would be health code inspectors wet dream too. Invest some time to drive north of there on 281 to the 410 or 1604 area for the nicer places. Between 410 and 1604 on 281 are a whole slew of eateries that are probably your safest and best bets to eat.
Not sure, but are looking for a great place to eat or a convenient place to eat? My most favorite place to eat in San Antonio is Paesanos and they have a location in Lincoln Heights on E. Basse Rd (somewhat north of the AT&T Center). It's not cheap, but it's moderately priced:
http://paesanos.com/Also, if you want to go eat where Tim Duncan loves to dine, then you can go to The Silo, a chic place that is somewhat moderate to expensive.
http://www.siloelevatedcuisine.com/I love dining there as a hidden treasure just east of the AT&T center on I-35 heading back towards Austin.