Skull Rock is located just next to the main road passing through Joshua Tree NP and there is a parking spot across the road from the rock. Therefore, the majority of the park's visitors stop there only for as long as it takes to take a picture of the rock and then leave to explore other parts of the park.
We, however, decided to go for a 1.7-mile (round trip) nature trail connecting Skull Rock with nearby Jumbo Rocks Campground. Multiple boulder piles located along the trail make this hike very attractive. We did not venture to explore any of them, but I could see how that would be a lot of fun.
Bartek, Anil and I, in front of Skull Rock:
During the hike we also saw another rock resembling face. We wouldn't have seen it, if we hadn't gone for a hike: