The park is covered with petroglyphs. I tried to get a few details out of the park ranger, but he only pointed me to the few that are marked on the map. (The way he spoke, there are many many more.)These are well identified with pull off areas and are marked on the map. The first pull off with the petroglyphs is about a 20 yard walk to some rocks that are well decorated.
The next site that is easily accessible is located much further down the road near the Jossie Morris Cabin. This one contains some of the more iconic images of petroglyphs in the park.
The only trail we both went on was the Box Canyon Trail. Located next the the Jossie Morris Cabin, this short .5 mile round walk is perfect for kids. The trail in winter is kinda dead looking, but during summer when all the trees are green, this would be a very pleasant place to go walking and exploring.
Trail- Split Mountain Trail
This trail I never finished. I had a few minutes and was wandering around and stumbled upon it. It is safe to say though, that it is not well maintained and is easy to loose track of the trail in some precarious spots. My word of advice here is to use judgement and if the trail disappears/ seems like it takes you someplace dangerous, turn around and find the trail again. This happened to me about 3 times while meandering close to a mile. But from this trail you do get a good look at Split Mountain along with Green River.