Two things, absolute best:
A. Mexican food (place and location)
B. Seafood (place and location)
In town May 2 to 6
Where are you staying? Will you have a car? Are you looking for hole-in-the-wall cheap authentic mexican or something more upscale? Tex-mex or "real" mexican?
For seafood I would recommend either Sandbar (downtown just off riverwalk, raw bar type of atmosphere) or Wildfish (North-central location @ 1604 and Huebner, upscale)
Staying at the Westin La Cantera resort.
Have a car.
I want Tex Mex and Authentic. Have time to eat both.
By far the best seafood place in San Antonio is Sandbar. Very small and not fancy in decor, but the dishes are out of this world. I am sure you can search on this site for it and read about its reviews.
My favorite mex joints are Mendez Cafe- it's south of downtown on Bartholomew just N of Southcross.
Guajillos is another favorite at 410 and Blanco
Also like Ceilito Lindo at Stone Oak and Huebner- authentic mexican
Both Ceilito Lindo and Wildfish are North Central, closer to your hotel than downtown.
Best Mexican in town is El Mirador on St. Mary's in King William historic district south of downtown. Great booz too. Don't know about seafood.