The Violet Trail (not to be confused with the Purple Trail) is a nice connector trail that links the Green Trail with the rest of the trail system. Violet is a nice beginner-friendly trail and is easily accessible from the park pavilions.
Violet starts opposite the Green Loop heading south past the radio tower and then splits a spur off to the left. The two options parallel each other and end at the same place though bearing straight at the split seems to flow a little better in the south/eastbound direction. Enjoy some nice S-turns on the way out, and save the other half of the trail for the return trip.