There are several areas with petroglyphs in the area around Canyonlands and Arches. The most famous of which is west of the Green River in Horseshoe Canyon. I was unable to work in a visit there but I did explore some areas along the Colorado River with Petroglyphs.
Areas with desert varnish (areas of very dark brown) often have petroglyphs carved on them (see the first two images and notice the desert varnish). Remember that Petroglyphs are carved in rock and Pictographs are painted on rock.
There are other signs of the past too. One my favorite on this trip was an granary high on a butte in Canyonlands National Park.
The Island in the Sky section of the park sits about 6000' high and about 2000' above the rivers. It is basically the top of a huge mesa. The extra elevation makes it a little cooler and also makes it a decent grassland. Although it is mostly flat there are still some hills and small buttes that can be found there. One of the small steeper ones is Aztec Butte. There is a great hike the slowly winds up the face of the slickrock and summits the butte. There one can walk the rim and take in both canyons and the mesa top. At several places tucked just beneath the rim are some overhangs. Some of which have granaries.
The one pictured here was my favorite. The overhang is right about 6' tall. The granary is in a corner, built of stones and is maybe 4-5' tall. Two small arches help frame the scene and the deep Taylor Canyon is visible beyond.
I was lucky to have the 10mm lens (16mm eq on a FF camera) to fit the whole scene in. This granary is on the north-northwest side of the butte, but I believe it gets late afternoon light on it in the summer months. I was not sure it would get it in October so I did not make the late afternoon trek back this trip. BTW this hike is a bit of a scramble toward the top and probably not for everyone, but for those who do not mind heights and a little bit of vertical exposure it is a great destination.
Side note- movie fans will see that a young Indiana Jones was adventuring around Moab area and Arches NP in "The Last Crusade".