We went running on the trails on the smaller side of the park (accessed from Thigiri Ridge Road) on a daily basis. Super safe now that its been fenced off and has gate guards. Great place to walk a dog if you have them, but people there need to be more considerate about cleaning up after them.
The bigger side of the park (off Karura) has a nice waterfall to hike down to, but don't go alone. Better for biking on this side of the park. There's a nice soccer pitch with tennis courts in the middle of the park which is the best place to park before heading in, particularly if walking.