Here are some local parks:
http://www.pwtsc.org/parks/
As far as safe, that depends on who, what, when, and where. As a general rule of thumb, if you have seen the park in the news for murder or rape, then avoid that park. A certain Dale City park comes to mind as one to be avoided if safety is your concern. Although, if you are running I am not sure that will be a problem. They generally prey on easy targets ;)
The Broad Run Trail is nice. Manassas battlefield has lots of trails and I would consider it safe during the daylight hours. So is the trail between Bull Run Park and Fountainhead which is on the FFX side of the PWC/FFX border.