In the San Antonio area:
Gruene TX is worth visiting - The
Gristmill Restaurant has decent food (and a nice view of the Guadalupe River), and the Gruene Dancehall (located next door) often has good live music. (ZZ Top shot a couple of "live" videos there).
There are also some interesting (albeit tourist-heavy) shops in the surrounding several blocks.
The town of Gruene intersects with
River Road, which follows the Guadalupe River through some great country - makes a nice afternoon drive.
Floore's Country Store in Helotes (just Northwest of San Antonio) often has good entertainment in a small venue.
The
Missions of San Antonio are interesting - They're scattered throughout the southern side of the city, mostly located along the old San Antonio River.
I would suggest avoiding the Tower Of The Americas - The admissions price has been raised to over 20 bucks apiece (just to ride the elevator to the top), and the tower restaurant serves pricey, mediocre food.
Other good food in the area:
Taco TacoPanchito's (Excellent for breakfast!)
225 Urban Smoke Barbecue - Quite possibly the best BBQ in San Antonio.
Honestly, there aren't many dangerous areas in town - and essentially none during normal daylight hours.