Visit the other missions, Missions National Park, the Old Governors' Palace.
It takes a little hunting around in this site, but brief info is there- Missions and Independence trip. See maps and go to the Mission Trails Map- click on it to enlarge.
You have almost a month, so order the guidebook linked in this site:

San Antonio

In one of the Mexican cafes order a Bohemia for me.

A long time ago they offered fried rattlesnake at the Zoo on Sundays- this probably has stopped.