Spend several days circling Yosemite's Clark Range, and the source of the Merced River, enjoying big mountains, open spaces, and cold blue lakes without the crowds normally associated with the words "Yosemite." The lack of crowds is because this is not an easy loop to reach, requiring either a really long approach hike from Yosemite trailheads or driving on twisty Forest Service roads. Another reason might be the 5 passes (3 over 10,000 feet) that the route goes over and all of the climbing (and dropping) that goes along with them. In any case, if you're willing to invest the time and effort, you will be paid back handsomely. Expect to spend 5 days on this hike, although a strong hiker could do it in 3 (but why?).
This guide covers the approach from the Quartz Mountain trailhead, which has the shortest approach hike. There are many other trailheads that can be used as a starting point, however, such as Chiquito Pass (the drive to which is all paved), the Fernandez Trailhead, or even Yosemite Valley itself (although that involves a 16-mile 5000' approach to the loop).
Entering Yosemite from the south, at Chiquito Pass, the trail meanders through the forest before reaching a junction to the Chain Lakes -- an excellent place to stop for a mellow first day's hike. From the Chain Lakes junction, the primary trail heads west and then north to Moraine Meadows and the South Fork Merced River, where the moraines are barely in evidence and the meadows not much more. From here, take the long climb to forested Merced Pass; Upper Merced Pass Lake is a lovely place to stay and the first reliable water since the South Fork Merced River.
After Merced Pass, you continue winding upwards and soon break out of the trees, getting great views of Red Peak, Ottoway Peak, and Merced Peak. Lower Ottoway Lake is heavily used, but for a reason: it is a stunning campsite, with a beautiful subalpine lake surrounded by peaks 2,000 feet taller. Upper Ottoway Lake, "only" 800 feet higher, is stunning too but for its austerity, with only tiny plants surviving amidst the talus. The camping here is limited and windy. From Upper Ottoway Lake it is another 800 vertical feet to Red Peak Pass, where a panorama across much of Yosemite unfolds.
The descent from Red Peak Pass and across the high open country of the north side of the Clark Range is gorgeous, and should be prolonged as long as possible, with wide-open country and expansive views. Camping and water are readily available through this entire area until the descent to the Triple Peak Fork of the Merced River. At the Triple Peak Fork you could head north to Washburn Lake and the High Sierra camp there, but this route climbs back up towards Post Peak Pass. You'll reach a big open bowl at 10,000' which is -- once again -- stunning. Once you finally decide to leave this basin, there is an 800-foot climb to the crest of the Clark Range and a traverse to Post Peak Pass, then a leg-jarring descent to geologically-intriguing Porphyry Lake. At this point you've left Yosemite for the Ansel Adams Wilderness and the trail gets noticeably harder to follow. After Porphyry Lake, the route descends once again into the forest and while water is available the camping isn't great until you climb back up to the Rutherford Lake area.
From Rutherford Lake, the route climbs up to Fernandez Pass (and a false pass first), and then plunges back into Yosemite towards Breeze Lake and its downstream siblings. Camping is good at the siblings. From here, descend back to Moraine Meadows, to the Chain Lakes Junction, and out across Chiquito Pass and to the trailhead.
When done as a 5-day hike, each day's distance is moderate (8-10 miles per day), but the altitude (mostly above 9000 feet), gain (1000-2000 feet per day) and cumulative exertion add up. Do not take this trip lightly.
Multiple starting points are possible, such as Quartz Mountain (shortest time to Chiquito Pass, but getting there involves twisty dirt Forest Service Roads); Chiquito Pass Trailhead (paved most of the way, but involving 2 extra miles and another 800' of gain/loss at the start/end); and the Norris or Fernandez Trailheads (both would add considerably to the approach hike) -- all in the Sierra National Forest south of Yosemite, making them the permitting agency.
You could also start from Mono Meadows, Glacier Point or even Yosemite Valley within Yosemite -- but these would add considerably to the hike and also to the amount of climbing involved.
The best time of year for this is August and September, after most of the snow has melted (and the bugs have mostly gone away).
My recommended itinerary (adjust or ignore as you like) would be:
Chain Lakes on night 1;
Lower Ottoway Lake on night 2;
Lake 10,000' (below Post Peak Pass, in Yosemite) on night 3;
Rutherford or Anne Lakes on night 4
... but it is hard to go wrong. The northern side of the Clark Range is full of open country and campsites everywhere. It is a good place to linger. The area between Post Peak Pass and Fernandez Pass is more forested and comparatively harder to find an excellent campsite.
Bear canisters, as always in Yosemite, are required.