I really enjoyed photographing the scenery just outside of town. I found very nice rolling hills, and the live oaks made for scenery quite different from home.
Another option might be to look for small towns with period architecture. I visited Fredericksburg, found it interesting (but not amazing, and a bit far).
The rolling hills and live oaks are practically anywhere north and west of town. For a small town with interesting buildings a lot closer, try Castroville, 30 minutes due west of downtown SA on US Hwy 90.
Almost anyplace downtown is good for people. If you like zoo pictures, SA has one of the best in the country. Venture into the West Side and you can find some spectacular color murals on the sides of buildings. Just south of downtown is the King William District, full of the mansions where the local industrialists and merchants lived in the 19th Century. Think "Mary Poppins" type Victorians.
Downtown has things already mentioned, like the Riverwalk and La Villita, but don't overlook the old Hemisfair park, where the convention center is now and the Tower of the Americas still stands. You can't miss the tower. (You can probably see it
from USAA)

This is directly across the street from La Villita and on an extention of the riverwalk. Near the south portion of the area is a row of victorian houses that survived all the urban renewal and were actually restored and incorporated into the Hemisfair park in 1968. They're still there and are offices and shops, so they are maintained. Downtown also has 2 or 3 notable and restored old movie palaces. Two old train stations. At least 3 churches built in the 19th Century. The San Fernando Cathedral (mentioned above) is 18th Century. Etc, etc.
The Institute of Texas Cultures, the McNay Museum, the Witte Museum ...
San Antonio is a great town. Zillions of tourists don't go there just for Sea World ...
One downside: this time of year will still be blazing hot!
Oh, and eat some fajitas!