Dale Ball features 30 miles of hiking trails near Santa Fe, NM.
If you can't get their by pedaling the major parking areas are: North, off Hyde Park Road on Sierra Del Norte; Central, the Nature Conservancy trailhead near the junction of Cerro Gordo and Upper Canyon Road, or; South, the St. John's trailhead on Camino de Cruz Blanca. But really, as long as you don't offend a property owner you can get on the trails practically anywhere.
http://www.tripleblaze.com/trail.php?c=3&i=1066