This is an easy run along the rim of the Rio Grande gorge. It starts from the Rio Grande Gorge Rest Area off Highway 64.
Mostly it's a doubletrack that follows the gorge south never more than a few feet from the edge. Particularly in the first half mile or so, there are a number of short side trails that lead to overlooks right on the rim down into the gorge. Several of these feature views of the Gorge Bridge with Wheeler Peak and the surrounding mountains in the background.
If you progress further south along the trail, you'll leave the hordes taking pictures of the bridge and have a good chance to see some bighorn sheep. The doubletrack ends at a parking area after 9.5 miles.
West Rim trail continues as a singletrack until it reaches NM 567 and the intersection with the Petaca Point Trail. Continuing a short distance down the road towards the gorge at this point leads to an overlook with a great view of the confluence of the Rio Grande and Rio Pueblo de Taos.
Also in the area, you'll want to do the La Vista Verde Trail, which heads through a valley above the Rio Grande, terminating at another overlook on the river.