Well - there's definitely no camping allowed on the top of Half Dome. Apparently several of the remaining trees on the top were (illegally) cut for firewood. This is the sign when you approach Half Dome from Little Yosemite Valley:
I looked at my map, and the 7600 ft level is maybe a little over a mile from Half Dome. I think there are some pretty good sites on the Half Dome Trail before the 7600 ft level, but I never saw anyone camping there. Getting a permit would be another matter. I don't think there's any permit that would allow you to camp there on the first night from Happy Isles. Maybe if you approach from Sunrise Lakes.
The regulations I've read are as follows:
Quote
Camping is prohibited in the following areas:
• The top of Half Dome
Camping is restricted in the following areas to campgrounds designated by posted signs:
• Little Yosemite Valley campground
• No camping is permitted in the area between Happy Isles and the junction of Sunrise Creek Trail and Half Dome Trail
The hard part is deciphering what the trail names actually are, because I've never really seen anything more than signs pointing to locations. I think there reference to Sunrise Creek Trail is what's on my maps as the John Muir Trail.
Short of camping on the Half Dome Trail I think it's either near the junction of Clouds Rest Trail and John Muir Trail (about 2.5 miles), or Little Yosemite Valley (about 3.5 miles).
You're probably better off calling the wilderness center for final clarification.