Mexican and BBQ. Taqueria Mexico on the south side (Somerset) is top notch. For BBQ Rudy's is good for chain stuff but if you want the real thing head out of town to New Braunfels, Luling or Lockhart for the good stuff. Shilo's deli in downtown is good German food. Chester's burgers are all over and all pretty good. Surprisingly there are good sushi and Indian places all over as well.
The riverwalk is ok if you like cheesy touristy stuff but for old school Texas type stuff head out to Gruene or Lukenbach or just take a drive up 281 to the hill country. Market Square in town is nice too.