Late May/early June is a great time to go because the waterfalls are at their peak and the flowers in the meadows are starting to bloom...but as others have pointed out, you'll probably not be able to stay in the Valley unless you're willing to stay in a tent cabin in Curry Village. People DO cancel reservations, though, so you might luck out if you try calling (or going on-line) 7-14 days before your trip.
But, you might consider staying in El Portal - that's about 35-45 minutes from the Valley, and it's drivable. I have friends that have stayed at Cedar Lodge there a couple of times and thought it was nice - there's other hotels, too.
Another option is the Redwood Cottages at Wawona - that's going to be more like an hour from the Valley. There's an area of privately owned homes there that I believe are actually within the boundaries of Yosemite National Park. A lot of them are available for rent - you can find more information on them at:
http://RedwoodsInYosemite.com. From that area you're close to the southern entrance to Yosemite and the Mariposa Sequoia grove.
Things to do (whether in May or September): Visit Glacier Point (though that could still be closed in May this year!), visit either the Mariposa or Tuolumne sequoia groves, take a hike out of Happy Isles at least as far as the Vernal Falls bridge, go to the Visitor Center and see the movie, walk to the base of Lower Yosemite Falls, walk to the base of Bridalveil Fall, have breakfast at the Ahwahnee Hotel, take the (free) Valley Shuttle all the way around...that's all pretty easy stuff.
If you're more adventurous...take the Hiker's Bus from Yosemite Lodge to Glacier Point and either take the 4 Mile Trail down to the Valley or hike the Panorama Trail (~8 miles) down to the Valley. I prefer the Panorama Trail myself - you get to see Illilouette Fall as well as Nevada and Vernal Falls.
There's also a hike to Mirror Lake and past Mirror Lake up to the Snow Creek Bridge and back down the other side.
As a previous poster stated, riding bikes around the Valley is a lot of fun.
Hope that helps.