My friend and I hiked Friedrich Wilderness Park in the morning and Eisenhower Park in the afternoon. Friedrich was small, but challenging. There are some fairly steep hills that were fun to climb, but unfortunately they weren't very tall. Still, it provided a good cardio workout.
My sense is this is one of the more popular spots in San Antonio. We were there on a weekday and there were a lot of people hiking and running the trails, so there wasn't much solitude.