Yosemite Advise Please

120 over Tioga Pass normally opens mid to late April. With the drought, there is no problem with May, much less June. You'll be fine.
You can ride through Yosemite in an hour or two. However, there is so much to see that if you're not in a hurry, I would plan on spending the better part of a day. If you finish and are ready to go, fine, but that's better than rushing and missing so much.
Here's a few to whet your appetite; some from 120 and some from 108 (Sonora Pass):
I know you have seen pictures of Yosemite (Ansel Adams made sure of that!) but it is a truly awe-inspiring place. In one day you can ride around, see the sights and take pictures. The best views of the Valley are at the overlook just before the tunnel on the way to Glacier Point and then at Glacier Point itself. We did that the first day (and then went back to the tunnel overlook on Day 2 to catch sunset, which you should try to see).
On Day 2 we did a short hike to the base of El Capitan. There is something about being at the bottom and then looking straight up that cliff face. Then go out into the meadow with your binoculars and try to spot the climbers. You'll have a whole new respect for them. Then we did short walks (more walks than hikes) to the base of Bridal Veil Falls and Yosemite Falls (the latter of which had no water flowing over it in October). All of those were worth doing. Unless you are a serious hiker or climber 2 days is enough to feel like you've experienced it.
In case you wonder about my sunset comment, here are photos we took from the tunnel overlook just before sunset when the sun was refracting through Bridal Veil Falls. Incredible! (These were taken with a cheap-*** point and shoot camera, zoomed in.)
The Best of Harley-Davidson for Lifelong Riders








