Angel peak is a 6991 ft summit in the badlands of northwestern New Mexico’s San Juan Basin just south of the town of Bloomfield. No trail goes to the top of the peak and I discourage any attempts to climb it because the peak seems to be made of soft dirt/crumbling rock susceptible to erosion and disfigurement . The Bureau of Land Management has preserved an area near the peak and along the edge of a nearby escarpment where a 6700 ft high plateau drops 500-600 ft down to a lower plateau creating a series of badlands along the drop. A 6 mile long dirt road travels near the edge of the escarpment giving rise to multiple scenic viewpoints. A good way to get continuous views of the badlands may be to hike the edge of the escarpment but I am not aware of any established trails in the area.
From the intersection of Routes 550 and 64 in Bloomfield, New Mexico, drive roughly 15 miles south on 550 and turn left (east) onto County Road 7175 (well graded dirt road passable by any car in dry conditions). Drive the road 6 miles to the end of it at the campground near Angel Peak. You can visit the viewpoints along the road.
Here are some pictures from the viewpoints along the road Badlands.
Zoomed view of the La Plata Mountains to the northwest of Durango, Colorado.
No fees or permits needed for visiting. For camping, see link above.