I dont know a lot about downtown restaurants, but heres a few good ones.
Downtown:
Liberty Bar, 328 E Josephine St, San Antonio, TX; great european food with with a texas twist thrown in, and a dining room that will give you vertigo. DEFINITELY GO HERE.
Mi Tierra, 218 Produce Row, San Antonio, TX; cool mexican place in market square, great atmosphere, great food if a bit overpriced
Blanco Cafe, 419 N Saint Marys St, San Antonio, TX; straightforward and delicious mexican food
Sushi Zushi, 203 S Saint Marys, San Antonio, TX; bastardized sushi, quite delicious
The area i frequent is about 5-10 minutes north of downtown:
Timos, 2021 San Pedro Ave, San Antonio, TX; cool little soup/sandwich/coffee shop. Great people working there, and i will be one of them come summertime.
Main Street Pizza, 1906 N Main Ave, San Antonio, TX; delicious pizza, great spot for lunch. I eat there atleast 3 out of 5 days a week.
Candlelight Coffeehouse and Winebar, 3011 N. St Mary's, San Antonio, Tx; cool 'swanky' coffee place with decent food. Very comfortable, my place of employment up until last friday.
Mon Thai, 4901 Broadway, San Antonio, TX; great sushi, ask for the back room with the glass ceiling. Not far from the Witte
Cappyccinos, 5003 Broadway St, San Antonio, TX; cool bar with good food, best hamburger ive found. Not far from the Witte, either
Paloma Blanca, 5800 Broadway St # 300, San Antonio, TX; great spanish food.
Oo, and if you didnt know already, that bodies exhibit is at the Witte.