Cathedral Peak (10,912') is one of the best beginner alpine climbs in the country. It is a priceless trip that culminates in a very dramatic summit needle that offers a complete panorama of beautiful wilderness. The climbing is fun and easy to protect, the rock is grippy and features cool knobs (consistent with the Tuolumne formations), and the approach is mild enough to make this alpine route fairly accessible.
From the Cathedral Lakes Trailhead, begin hiking on a well-worn hiking trail toward Cathedral Lakes. At .5 miles, find a subtle trail branch to the left. This is the climbing access trail. It is well-worn, but it is also less obvious than the Cathedral Lakes trail, so keep your eyes peeled. After another mile or so, you'll be near the base of Cathedral Peak. Continue up the increasingly steep slope until you reach the base of the wall. You'll find the base of Cathedral Peak's southeast face 50 feet down and left.
There are a number of different ways to wind up this wall, and this is just one recommended route:
There is no rappeling anchor for the summit block. Simply downclimb the east side, and circle back around heading north across slabs. Stay close to the ridge, and keep your eyes open for the narrow passage down. Downclimb a short fourth-class section, then follow a well-worn descent trail back to the base of the wall.