Mt Lyell is the highest mountain in Yosemite (3997m), followed by
Mt Dana (3979m).
The trailhead is located on the east side of Tioga Pass (right by the toll entrance station) at 3,033m of altitude. The total hike is 9.3 kms roundtrip. The trail is not exciting at all. The first hour and a half is a steep approach to a plateau. From the plateau to the top it is an even steeper scramble on rocks. There are several use trails that climb up the northern face of Mt Dana, but most hikers prefer to hike the ridge to the east, in order to have views of Mono Lake and the little lakes below the mountain. If you follow this route, it is going to take you about 45 minutes to reach the ridge, and then one hour to the to the top (the trail you make is the trail you take). The whole hike takes about three hours plus stops. (My best recorded time was 2h13' in 2012 on a very dry year with no water/snow)
The reward for this rather dull hike is a magnificent view of the lakes. Coming down takes about 2 hours. So the roundtrip hike takes about five/six hours.