The area around the airport is not conducive to great dining, but here are some places.
For Mexican, try Guajillo's,
www.guajillos.com. Their tacos al pastor were mentioned in Epicurious and Huffington Post a while back.
Not much in the way of brasseries, but some of the best Naples-style pizza is at Dough Pizzeria.
www.doughpizzeria.com
There's a cute Vietnamese place not far from the airport, Pho Thien An. They serve some Chinese dishes, but stick to the Vietnamese.
Also, try the contemporary American options at Bin 555,
www.bin555.com. Thoughtful wine selection and well-made dishes.
Enjoy your time in San Antonio. There's some excellent dining here, but you have to seek it out.