Just over the border in Arizona, but we claim it as part of Utah
They can have the South Rim.
If you want a taste of what the park was like before paved roads, safety approved overlooks and way too many people; I'd suggest the 17mi unpaved road to Point Sublime. Check at the Ranger station for any closures but well worth the drive. Take lunch, spend the day and imagine it's 1940. Take all the little turnouts and walk out onto the overlooks and you will have a feel for what the early tourists enjoyed. Sunset at Point Sublime is to die for. BTW the lodge restaurant is an absolute must for at least one dinner out $$. Excellent food and a beautiful setting.