It's tough! We've had good experiences at Byrd Park, away from Barker Field-- or close enough to play "dog park tv," where we lavish her with treats for looking at the dogs but not freaking out. The best spot we found when we lived on the Southside was Drewry's Bluff. It's a good loop through the woods, some river views, and almost never any other dogs. Only problem is that the trail in is the same as the trail out, so if you run into trouble there you don't have as many ways to dodge. On the north side, Bryan Park is good at off hours, especially if you stick around the lakes and are decently good at spotting dogs far off.