Wheeler Peak is the highest mountain in New Mexico, but it is not a particularly spectacular or interesting peak. The Sangre de Cristo Range in northern New Mexico is largely a high but gentle range of rounded summits with unusually high treelines--very few other places in the world have forests above 12,000 feet. The arbitrary Colorado-New Mexico boundary passes just south of 14,069' Culebra Peak, meaning New Mexico just misses out on getting a fourteener, and Wheeler Peak isn't even the furthest south major rocky mountain peak. That honor goes to Truchas Peak (13,103'), just a shade lower than Wheeler and the southernmost thirteener in the American west.
The main reason people visit the Wheeler Peak vicinity is to ski at Taos Ski Valley, a world-class ski resort on the neighboring peak to the south. Wheeler's summit is visible from the eastern reaches of the ski area, and the ski area road provides paved access to the usual trailhead for the peak.