Between Price and Moab is the San Rafael Swell and the Green River Desert you could easily spend a week there
These websites certainly aren't the cats meow for each location but give general idea a quick search will reveal more you could link several of these togethor on the way down
Rochester Creek Panel
https://www.roadtripryan.com/go/t/utah/san-rafael-swell/rochester
Buckhorn was panel
http://www.utahoutside.com/2012/05/explore-buckhorn-wash-in-the-san-rafael-swell/
head of sinbad panel one of my favorites
http://www.sanrafaelcountry.com/san-rafael-swell-head-of-sinbad.html
on this website there is a maps section that may be helpful for several of these sites
swaseys cabin
http://www.sanrafaelcountry.com/san-rafael-swell-swaseys-cabin.html
black dragon canyon
http://www.sanrafaelcountry.com/san-rafael-swell-black-dragon-wash-rock-art.html
Great Gallery this is one of the best in the world a bit out of the way but imho worth it
http://www.hikingwalking.com/destinations/ut/ut_se/canyonlands/horseshoe_canyon/horseshoe_canyon_detail
In Arches National Park make sure and due the primitive loop hike at the end of Devils Garden as well as Delicate Arch not sure how much you hike but we can do both in the same day as well as see the other main points in the park
https://www.nps.gov/arch/planyourvisit/upload/ARCHmap.pdf
Canyonlands National Park
Island In the Sky Mesa Arch, Shafer Trail for the ride back to Moab
https://www.nps.gov/cany/planyourvisit/maps.htm
Dead Horse Point on the way to Island in the sky anytime great sunrise, sunset super great, night sky if clear awesome
https://stateparks.utah.gov/parks/dead-horse/
Needles District
https://www.nps.gov/cany/planyourvisit/needles.htm
Hike to Druid Arch, going through Chessler Park, return through the Joint and Devils Kitchen long day but so great. You can cut substantially by looking at map and turning around or taking variations back to trail head if you hike this is stuff you don't want to miss
https://www.nps.gov/cany/planyourvisit/maps.htm
Gemini Bridges, Utah 128 through Fischer Valley, Las Sal Mountain Loop Road the list is endless out there
Best breakfast in town is at the Moab Diner