Just to say that you did it the River Walk and the Alamo are ok, but keep in mind that they are extremely touristy. Over the years I have been to many places on the River Walk and would just suggest you stay away for dinning. Or entertainment. I really hate that place. With a burning fire, I hate that place. If you are staying in town, the Alamo Cafe is straight up TexMex that is ok. Acadiana is my favorite "local" place to go, it's cajun food that again, isn't the best in the world but I enjoy it. They stopped decorating the place in the 80's so it looks kind of rough. Pearl Stables is another place that I would recommend, I think there are several restaurants there, probably my favorite part of SA.
If you have access to a car, might I suggest leaving the city limits? Within an hour drive you have some seriously awesome places. Gruene, TX is home to the Gristmill. One of my favorite restaurants, and Gruene hall is right there, lots of fun. Or you could make the trip out to Lockhart or Luling for some BBQ, in order Smitty's, Luling City Market, Black's, Kreuz (pronounced Krites) are some of the best places in the state and they are all within driving distance of each other. Depending on when you are dining Black's and Kruez are the Safest bets, Smitty's and Luling City Market tend to sell out.
Houston is a totally different story there are dozens of places that are stiller, most of them have great write-ups.