Memorial Park is Houston's Central Park. Located west of downtown (south of I-10, east of I-610), Memorial Park is the place to go for outdoors recreation inside the loop. Some days it feels like everyone in Houston is out on the jogging trail, mountain biking, playing tennis, or just enjoying the day.
Memorial Park has the best public golf course in Houston, tennis courts, baseball fields, volleyball courts, picnic areas, and the Houston Arboretum.
The Seymour Lieberman Exercise Trail is a crushed-granite 2.93 mile loop that circles the golf course in Houston's Memorial Park. There are several water fountains (for you and your dog) along the way, along with two sets of porta-potties. There are only two road crossings (the entry and exit to a parking area), but the entire trail is next to busy streets, so you never really feel like you are getting away.
The mountain biking (or Ho Chi Minh) trails in Memorial Park are the best singletrack trails inside the Loop in Houston. They get very busy on weekends and after work, so you have to be very careful on them, whether you are walking your dog, trail running, hiking, or mountain biking.