Kristen,
Are you going to be six days and five nights or seven days and six nights?
Are you going in at May Lake and coming out at the Yosemite Creek trail-head on highway 120?
I suggest that you plan your stops based more on the availability of water and less on how much flat ground you can find. There is always somewhere to pitch a tent even though in your case there will be several.
Day 1. Hike from May Lake parking to the fork of Cathedral Creek and camp at the trail junction to Poly Dome Lakes and McGee Lake. This is about five miles and pretty flat.
Day 2. Up and over the the Tuolumne Peak area and down to the South Fork of Cathedral Creek. You will be on the South Fork for about a mile and good camping should be all over the place. This hike will be about five miles with 1100' up and about the same amount down.
Day 3. Hike to Ten Lakes. There are two larger lakes along the trail so you have to pick which one to stay at. They are about a mile apart. This hike is about 4 miles long and has about 1000' elevation gain.
Day 4. Stay at Ten Lakes.
Day 5. Stay at Ten Lakes.
Day 6. Hike out to the Yosemite Creek trail-head. This hike is bout five miles long with 1000' up right at the start. The junction to Grant Lakes is at the top of the assent so those that want to can rest while those that want to can day hike to Grant Lakes.
If you have one more day then everybody could go to Grant Lakes for one night or spend another night at Ten Lakes.
Bears can be active on your entire route so be sure everybody really follows food storage procedures especially no food in tents.
Old Dude