I have two favorite National Monuments in Utah, Hovenweep and Natural Bridges. Hovenweep has some of the finest and most unusual structures from the early people including an easy and wonderful loop hike near the campground. It's a big, but wide open campground. Spent a night in a tent in a long thunderstorm there once. Exciting. First slideshow.
Natural Bridges National Monument has some beautiful scenery, several fine hikes, short and long, a few ruins (if you can spot them), and as the name says, some inspiring and huge natural bridges. The campground there has only 13 spots and will not accommodate large campers or trailers. There's plenty of places to just wild camp all around the area. It's an International Dark Sky area also. The stars come to the horizon all around. Second slideshow.
Natural Bridges National Monument has some beautiful scenery, several fine hikes, short and long, a few ruins (if you can spot them), and as the name says, some inspiring and huge natural bridges. The campground there has only 13 spots and will not accommodate large campers or trailers. There's plenty of places to just wild camp all around the area. It's an International Dark Sky area also. The stars come to the horizon all around. Second slideshow.