Sure, this isn't really a mountain, but it would be a shame for it not to be included here for you to try this wonderful hike. Sentinel dome is one of the many domes or exposed granite features of Yosemite Park.
The panaromic view from Sentinel dome is in my opinion the best in Yosemite, period. Clouds Rest has a wonderful view, but it is on the "end" of the valley, whereas Sentinel dome is right in the middle of the valley on the South wall and has unobstructed 360 degree views of everything in sight.
The hike itself is easy, only a couple of miles from the trailhead off of Glacier Point Road. It follows a wooded path that leads to the base of the dome with another 50 yard easy scramble up the gentler face and you're there. The top is barren as with most Yosemite domes, but there are a few noteworthy features.
One is an ancient Jeffrey Pine tree that has been long dead but remains twisted and tortured by the elements (fire, rain, snow, wind). It is an amazing and unusual site on the dome.
There is also a round stone compass on the top of the dome in the ground that is etched with all of the surrounding features and peaks from this vantage point.
A good topo map of the area can be seen here - topo map
Usual Yosemite rules apply to camping, fees, permits, etc. As with most of Yosemite, during winter (November-May) travelling can be challenging and conditions may require technical gear (crampons, ice axe, etc.) that is not needed other times of the year.
From Yosemite Valley, take Highway 41 (Wawona) and climb out of the valley for about 9 miles to Glacier Point Road, turn left and drive on for 13 miles and then you will see the Sentinel Dome trailhead on the left side of the road.
$20 per vehicle, good for seven days.
Black bear restrictions:
If you drive a private car into the park, you must adhere to strict regulations on the storage of food, because black bears in the park have grown accustomed to "liberating" stored food from vehicles, at any time of the day or night. If a bear breaks into your car to steal food (even candy-bar wrappers constitute "food"), you are liable for $500 or more in fines.
Overnight road closure:
Although the official Tioga Road winter closure (between Crane Flat and Tioga Pass) is in effect only between mid-November and late-May, the park service prohibits overnight parking anywhere on Tioga Road after October 15. The area is open to dayhiking until the official road closure, but I guess the park service fears that a storm can unexpectedly close the road at any time, and leave you and your car stranded!
If you plan on crossing Tioga Road in late fall (before it closes) or in late spring (after it opens), carry tire chains in your vehicle.
Sad News - The Pine is gone...
Yosemite National Park News Release
August 18, 2003
For Immediate Release
Famous Jeffrey Pine Falls on Sentinel Dome-Yosemite National Park
Carleton Watkins photographed it in 1867. Ansel Adams photographed it. It is among the most photographed trees in the park--the subject of numerous postcards over the years-- and a beloved icon to millions of visitors to Yosemite.
Sometime in the last week, it fell to the ground. The Jeffrey pine, perched on the summit of Sentinel Dome, was a dramatic image of which few could not stop and snap a picture.
The pine died in the severe drought of 1976-77, although people attempted to save it by bringing buckets of water to it.
The National Park Service does not know what final stress caused the tree to fall, but severe storms in the Sierra Nevada in early August may have contributed.
The tree's life, death, and fall are part of a natural process. However, many will miss the Jeffrey pine that stood and welcomed them to the summit of Sentinel Dome.