That's interesting. My mom went to Yosemite when she was 7 months pregnant--June and I was born in August.
Early June is not as crowded as mid-summer, especially if it's not the weekend.
I like rafting on the Merced River. You can rent a raft at the Bike Shop/Ice Rink in Curry Village, float down, and they take you back up downstream.
I like hiking the Valley Floor trails that run along the north and south side of the Valley. Here's a good map of trails
http://www.yosemite.ca.us/maps/yosemite ... p_2006.pdf
It's crowded near the falls, Mirror Lake, Happy Isles, but the other trails are uncrowded.
Also the Pohono Trail that runs along the South Rim of Yosemite Valley. Start at Glacier Point or Taft Point or Sentinel Dome. Great views along the rim.
Hiking Tuolumne Meadows is nice, although there are a lot of people it's not as crowded as the Valley.
Nice trails in Wawona Grove. It's crowded though.
There's a few obscure Forest Service campgrounds west of El Portal off of Highway 140. There may be some on 120--I don't go that way--sorry. Check the Forest Service website for Sierra National Forest.