For summer (these are from memory, so there may be minor mileage gaffes):
1 - Sentinel Dome and Taft Point - moderate 5 mi RT, lovely and dizzying views of the Valley and High Sierra; Glacier Point Road.
2 - Mt. Hoffman - requires some minor route finding skill, but a great 7 miles RT. A good deal is steep and strenuous, spectacular views. Off Tioga Road. If rain/thunder threatens, turn back. Good practice for Mt. Dana. Trail passes Sunrise High Sierra Camp.
3 - Upper and Lower Cathedral Lake, side trip to Medlicott Dome at northwest corner of Lower Cathedral - simply gorgeous, about 10 mi RT, moderate; Tuolumne Meadows.
4 - Gaylor and Granite Lakes Basin, about 5/6 mi RT, starts strenuous but this is short, then moderate with some easy cross-country if you use a topo map. Tioga Hill, old mines, gorgeous cirque lakes. IMO, the fastest and easiest way to see extraordinary alpine scenery in the park. At Tioga Pass. Watch weather for thunder - some exposed areas on this walk. Probably a good jumping-off point for peak bagging to the north.
5 - Pothole Dome - easy then moderate short walk/scramble onto low-slung dome with interesting geology, really fine views. West end of Tuolumne Meadows.
6 - If you have a bunch of stamina, Waterwheel Falls and back (about 16 mi RT, strenuous due to length). All the great falls of the Tuolumne River in one hike, starts at the Meadows. Note - the way back is uphill. Passes Glen Aulin High Sierra Camp.
7 - Mt. Dana - 6 mi RT, 3,100 foot elevation gain, very steep and strenuous, start early and give yourself a couple days to acclimatize at Tuolumne Meadows or better yet, Saddlebag Lake / Tioga Resort - the top of this summit is over 13,000 feet MSL! Start early as possible, right at Tioga Pass entrance station (park at Gaylor Lakes parking lot, Dana trailhead is immediately east of station on south side of road - not obvious or signed, but just walk into woods at large pullout at summit, and you will pick up the trail near some glades and continue past some small lakes). If rain threatens, turn back - this is not the place to be in a storm. If you get up to the area known as "Oh-My-God Ridge" just below the Summit, the views become utterly jaw-dropping as the entire Central Sierra and Mono Lake area come fully into view. Pikas and Marmots are your company at the top.
On this one, some minor route-finding and courage and knowledge of how to follow the trail is useful. There are several accounts of this hike on the web that are worthwhile reading, and some of them make it *sound* harder than it is - nonetheless, it requires care (scrambling up and down steep talus and rocks can be taxing) and strength and determination, and it is best to test yourself beforehand on somewhat lesser hikes before attempting this one.
All of these are genuinely rewarding and amazing. Not a dud in the bunch.
Wilderness forever,
Bruce Jensen