Dana Meadows is at the far eastern edge of Yosemite, just inside the Tioga Pass entrance along Tioga Road (which skirts the northern edge of the meadow, just beyond the right edge of this photo). The ranger who spends his day cramped in the admission booth here, breathing auto exhaust and wondering why he got that doctorate in forestry to run a cash register, has a view very similar to this one, so you needn't feel too sorry for him.
Dana Meadows is at the highest point along the Tioga Road, with an elevation just under 10,000 feet (3,031 meters, to be exact). Mammoth Peak is 12,117 feet (3,693 meters) high, making it the sixth highest peak in Yosemite. (Mount Lyell, at 13,114 feet/3,997 meters, is Yosemite's tallest.)
Tioga Road, the only access to Dana Meadows, usually opens around the first of June and closes again by early November. The meadow is worth seeing anytime the road is open. It's perhaps at its most scenic early in the season, when the meadow is green but you can still see snow on the surrounding mountains - somewhat like the photo above, which was taken in early July. It's beautiful late in the year, too, when the grass has turned brown and Nature is closing up shop for the season, and the almost palpable approach of winter leads you to start wondering whether or not you packed your tire chains.
There are no trails through Dana Meadows, although the Gaylor Lakes trailhead is just across the road.