Downtown has a nice plaza around the old courthouse, and is a good area for street scenes.
There are some missions along the border to the east; check the visitor guide for details. I've never had time to make it out there during daylight. I don't think they're on par with the ones in San Antonio though.
The scenic drive on Franklin Mountain is worth the view, as is the Transmountain highway. This is from the rest area on the west side:

Sorry I wasn't more help. Most of my trips don't leave much time for exploring.