Primitive camping, but free and quiet on West side. Long drive in. Bring water. Better for climbing: Moby Dick (III 5.8, 6 pitches). Highly recommended! Warpaint (III 5.10, 5 pitches) is excellent as well.
Pay camping with amenities on East side. Busier, but good bouldering around campsite. Access to South face;
Beeline (5.9R, 2 pitches) In the 5.10 range, Welcome to the machine (III 5.10c/d, 4-5 pitches) is well protected, and excellent.
Be advised, the climbing at Cochise is VERY SERIOUS, many of the climbs (even the lower grades) involve off-width, chimneying, and/or runouts/scary gear, old bolts, tied-off chickenheads, and licheny rock.
The ones I recommended are pretty well protected (for Cochise )
Have fun! Spot a Coatimundi for good luck!
Erik