Mt. Starr is easily one of the best quick and easy summits in the Eastern Sierra. The trail is mostly runnable all the way to Mono Pass before a tough, off-trail scree and talus scurry up to the summit ridge where you'll enjoy insane views of the more impressive peaks in Little Lakes Valley.
From the Mosquito Flat trailhead, follow the Mono Pass Trail. At the junction at 0.5mi, vear right toward Mono Pass (left goes up Little Lakes Valley to Morgan Pass). The trail climbs a series of rocky switchbacks up Mt. Starr's eastern flank, passing the Ruby Lake junction before entering increasingly exposed scree and granite terrain. Continue up the steep, rocky canyon to Mono Pass (12,060 ft) at 3.5 miles. From the pass, leave the trail and head northeast up the steep scree field to the summit ridge. The upper mountain rises roughly 800ft in under a mile, sustained and loose. Follow the ridge to the true summit at 12,835 ft.
Snow can linger late in the upper canyon near Mono Pass and on the summit approach. Water is available in the valley and along the lower trail; above the pass it's dry. The Mosquito Flat parking area fills early during summer. On weekends, arrive before 8am or after 4pm, or expect to park down the road.