Freedom Park...Charlotte's answer to Central Park.
Okay, so maybe that's a tough comparison, but Freedom Park is a great place for running, walking your dog, picnicking, playing frisbee, etc.
There are numerous walking/running paths winding through the park, a lake in the middle to stroll along, and plenty of places to sit and take in the scenery and poeple watch.
The grounds are nicely landscaped, and the colors in the spring and fall make it a great escape from the busy streets of Charlotte.