Because you can't visit San Antonio and not see the Alamo.
Austin is about an hour drive away from San Antonio. If you're looking for a fun night out, go to sixth street and bar hop. Austin is known for their BBQ as well; Franklin BBQ is one of the best spots, but be prepared for a long wait (it's worth it).
Plan a day trip and tube down the Comal River to get some views of the Texas Hill Country.
Take a boat ride on the Riverwalk, shop at the stores, and grab a bite to eat overlooking the San Antonio River.