Beginning just south of the village of Pilar and stretching several miles north, Orilla Verde Recreation Area ($3/car) is public land along either side of the Rio Grande, used primarily as a put-in or haul-out for rafting, but you can camp on the riverbanks as well—Petaca and Taos Junction have the best sites ($7 per night).
The Vista Verde Trail runs about 1.2 miles one-way along the west rim, an easy walk with great views and a few petroglyphs to spot in a small arroyo about a third of the way out; the trailhead is half a mile up the hill from the Taos Junction Bridge, on Highway 567 (turn left off the highway in Pilar and then follow signs into Orilla Verde).
Stop first on the main highway at the Rio Grande Gorge Visitors Center for maps and other information (Hwy. 68, 575/751-4899, 7:45 a.m.–4:30 p.m. daily June–Aug., 10 a.m.–3 p.m. Fri.–Sun. Sept.–May).
Across the road, Pilar Yacht Club (Hwy. 68, 575/758-9072, 8 a.m.–6 p.m. daily Apr.–Nov., 9 a.m.–2 p.m. Thurs.–Sun. Dec.–Mar.) is the center of the action, serving food to hungry river rats and functioning as an office for a couple of outfitters; TNM&O buses running between Taos  and Santa Fe  can also stop here if you ask.
You can also go horseback riding nearby with Cieneguilla Stables (505/751-2815, melcieneguillastables [at] hotmail [dot] com), starting at about $40 per hour.