In Yosemite, there are trips that get to above tree line lakes entering Tuolumne Meadows. You could go up Rafferty Creek to the Vogelsang area and spend time checking out the lakes, peaks, and passes in the vicinity like Fletcher, Vogelsang, and Bernice. Another option is to enter Lyell Canyon and head over Donohue Pass to the Marie, Davis, 1000 Island Lakes areas. You could also enter Agnew Meadows from the east side and check out the Minarets area. Though not actually part of Yosemite proper, the area is very scenic. Generally, getting a permit for Lyell, Raferty, or Agnew Meadow might be an issue as they are all very popular, so it is good to have several options if you can't get a permit for your 1st choice.
Ten Lakes is much easier to get a permit and makes a nice weekend hike. Most camping spots in the area are below treeline, but there are many knobs with good views of the area and down into Tuolumne Canyon. You can extend the trip length by heading to Tuolumne Peak and May Lake/Mt. Hoffman, etc., with a mix of forest trails and above treeline peaks and knobs.
Dana/Mono/Parker is an easy to get permit, but I don't recommend going over Koip Pass on the 1st or 2nd day due to altitude (12,250) unless you are confident in everyone's ability to handle it on day 1 or 2. But entering Lyell and looping back over Koip could work for 4-5 days, giving a few days for acclimation before tackling Koip.
Be aware that if you want to use a shuttle to get back to your car that the last day for the hiker's bus is 9/14 and that YARTs runs weekends only in Sept. The Yosemite Park Tuolumne Shuttles also shut down sometime in Sept, so call ahead if you are thinking of relying them.
It's a very dry year out here so be prepared to carry water on stretches between lakes and sizable creeks.