You can't camp near May Lake except at the backpacker's campground at the south shore.
There is a decent flat sandy spot at the saddle at the summit of the mystery trail--you'll need to haul water, either from the creek that the trail crosses before the climb or the one that the switchbacks follow. There are also spots near the saddle between the McGee/Cathedral side and the South Fork Cathedral creek. You can also drop down a bit into the South Fork side onto a broad granite "ramp" from this saddle--this should have some water in a small tarn--but no guarantees this year. Lastly, there were a few sandy spots in whitebark pines along the ridge between this saddle and the south summit of Tuolumne Peak, but it's a bit steeper here so it's harder to find a large flat area.