We did a trip exactly like that a few years ago. Started in Leavitt Meadows, and spent the first night at Fremont Lake. Second night took us up to Cinko Lake, just as it was icing out. And the third day was over towards Harriet Lake, and then back down into Piute Meadows...but when we found the mosquitoes down there we hiked back up into Long Canyon to get above them. That worked, and then we were able to hike out on the last day. Great trip.
The whole trip log is here:
And then the following year we did the hike up out of Twin Lakes to Peeler Lake ( that's a long, hard climb) and from there we did the whole loop into Kerrick Canyon, Benson Lake, Matterhorn, etc.. But that was a week-long adventure. YOu could just as well do the shorter version, from Peeler going down into Kerrick Canyon, then heading up to Snow Lake, Crown Lake, and back out. Lovely country there as well.
Here's the trip log for our longer version of this one:
And you can read more about these hikes on our website, backpackthesierra.com