We chose to go on St. Paddy's Day weekend and I highly recommend this especially because they turn the river green in the morning and then they even have a water parade. I am not saying it is the fully-decorated type of parade, but more of a leisurely stroll of boats throwing out beads. We actually went to an English Pub (Yes, I know there are plenty of Irish ones but they were packed and we bought their tickets to ride their float and have a free drink for about $20 pp). So, armed with plenty of beads to throw, we got to tour the waterways. On certain days, they also have arts and crafts fairs along the Riverwalk and you can buy a glass of wine at the local wine spot and take it on your walk in a plastic cup. We walked to the Alamo, which was interesting in itself, and then did the fun touristy things like go to Ripley's believe it or not, the big outdoor mall, and the souvenir shops. We also did a ghost walking tour which was pleasant, but not the creepiest I have been on. They also have a dining-on-the-riverboat option that might be worth checking out. If you need to leave the Riverwalk area, you can head to Six Flags for the kids as well.
Places to see:
The San Antonio Riverwalk