"Legend Rock State Archaeology Site is one of the oldest and best examples of the Dinwoody rock art in the world" according to the Wyoming State Parks brochure. There are over 300 individual petroglyphs, and some are thousands of years old. The Wyoming Parks web page for Legend Rock can be found here.
To see this site, your excursion must start at the Hot Springs State Park visitor center in Thermopolis. First, you are required to register with your driver's license and the license plates of your car, and then you receive a padlock key to the gate of the site (all this helps prevent vandalism). If you are not returning to Thermop, there is a place outside the gate to deposit the key when you leave Legend Rock.
If you are going to visit Cody and then Yellowstone National Park, Legend Rock is on your way, about eight miles off of Highway 120. Travel 21.7 miles from the visitor center to the second turn off to Hamilton Dome. The first sign for Hamilton Dome, about nine miles toward your destination, looks like this:
The sign below says, "High Island Ranch & Cattle Co." There are no signs for Legend Rock on Highway 120.
As soon as you make your turn, you will cross this cattle guard. The street sign says, "W Cottonwood Cr."
Just down the road a piece is the first sign informing you that you are on the right road. It reads, "Legend Rock State Historic Site The Petroglyph Site Is Open To Supervised Tours Only, By Contacting: Hot Springs State Park, 864-2176". However, if you follow the instructions above, a supervised tour is not necessary.
Stay on this road for 5.5 miles until you reach a fork in the road where the paved road continues left, but you need to turn right onto a gravel road. The sign below will indicate where you need to turn.
After crossing two cattle guards, veer left as the photo below indicates. This road will take you to the large green gate entrance which is just a few hundred yards from the the left-hand turn below.
To the left of this pedestrian entrance (barbed wire now blocks it) is the large gate which will need to be unlocked. After you drive through the gate, it must be locked behind you (so keep the key until you leave).
On your way to the parking area, take a moment to stop your vehicle and get out to enjoy the look of the valley below. The photograph below was taken right next to the road, which is also the top of the cliff on which the petroglyphs are found.
Next to the parking area (upper right-hand corner of the shot below) you can see the restrooms.