Fantastic views, almost guaranteed solitude, 900' of solid granite, a great route at 5.7 (or more likely 5.9). The real crux is route-finding on P3.
Valley Approach: Climb Royal Arches with an early start, then hike to the base of North Dome.
Tuolumne Approach: Hike in from Porcupine Creek.
From the base of the south face, hike up a 3rd class ledge angling from bottom left to top right, aiming for the large corner in the centre of the face.
160ft (5.6R) up slabs, small cams at your feet on ledges, then up crack to tree belay.
100ft (5.6) up left facing corner to belay on one of two trees.
160ft (5.7) route-finding crux, ignore the many slings further up the corner in easy terrain. Move up the corner for only ~20ft, step right onto a sloping ledge and continue right almost above the belay, then swing up and over on to the face, contour 10ft to a crack, then follow up to belay above bushes, cams in crack. Rope drag is a problem. All moves can be protected with cams, but you'll likely need a mid-belay just up on the face due to rope drag.
160ft (5.7) Continue up the crack with good gear, near the top it narrows and small nuts or cams are required, before a 20ft run-out slab with 5.6 friction leading to a bushy ledge. Belay with cams in corner.
160ft (5.7) Up awkward chimney with awkward move to exit at the top, then up to right facing corner with beautiful (but strenuous) lay-backing). Tree & cam belay.
160ft (5.7, more like 5.9) Similar to previous pitch but steeper. Up awkward chimney, then strenuous lay-backing. Stop for a semi-hanging belay when you're ready.
100ft (5.5) Presuming you belayed beyond the steepest section, continue up the easing corner, up and short step and follow the corner around to the right to a stance, cam belay.
100ft (5.6) Climb out to the left above the crack to a friction slab, make sure you place gear in a small crack line in the face to protect the final 20ft run-out slab. Then 50ft of 4th class friction to belay at large tree.
Unrope and continue up 3rd class terrain to the summit.
Valley Descent: Quite epic, descend the North Dome gully.
Tuolumne "Descent": actually ascent, hike up the trails to Porupine Creek.
FA: Mark Powell & Wally Reed, 1957
FFA: Mort Hempel, Irene Ortenberger & Steve Roper, 1960