I usually go off of the main walking trail and do an actual hiking trail. If you walk quickly, you can finish it in about 30-40min. If you park at the lot off of Grindstone, instead of going over the bridge onto the main walking trail, there is a slight path in the grass to the left before you get to the bridge. This is the hike that I enjoy most at this location. The first fork in the trail I always turn left.
Currently runs just off Providence Rd (behind Mizzou Arena) to Old 63 Hwy (about a half mile south of Stadium). The bridge near Rock Quarry Rd is under construction currently, and they are under construction to add a section to the Old 63 end that will cross under Old 63 to the Grindstone Nature Park (and beyond?). Mostly gravel, and winds through some woods and near Hinkson Creek, and contains a few bridges. Can get muddy in some areas from rainfall.