North Dome is a good all day hike that culminates in a face to face view of Half Dome that it hard to beat anywhere else in the park.
The trail starts at Porcupine Creek Trailhead off Tioga Pass. Wind through mixed-conifer forest for 0.7 miles (1 km) on a paved path, and cross Porcupine Creek. At each of several trail junctions, follow the signs toward North Dome. The trail passes through a small grassy meadow and descends along a ridge. Near the end of the hike, descend steep rock steps to the base of North Dome. Then climb the dome’s rounded summit to take in a magnificent view of Half Dome and Yosemite Valley below. On the return trip you can take a short detour on a side trail, 0.3 mile (0.5 km) to an unusual natural arch, Indian Rock. Be sure to take plenty of water as this trail is very exposed at parts and there is not much available along the way.
Since this hike is located off Tioga Pass, the only/best time to hike it is late May-early October while the road is open.
There are 2 other alternative trail routes if the Tioga Pass is closed, you start at the Upper Yosemite Falls trail and continue along the Snow Creek Trail to North Dome and Indian Rock.
The other is to start on the Snow Creek Trail via Mirror Lake loop (which is a slog of a trail) but if you’re into that kind of thing, you will be thrilled at the countless switchbacks.