The best views of Yosemite are in Yosemite Valley, which is open year around. You'll miss the High Sierra along the Tioga Road and Glacier Point.
The Tioga Road doesn't usually open until May or June--sometimes July, so you'll have to visit in high season for that:
http://www.nps.gov/yose/planyourvisit/tiogaopen.htm
Late May/early June is good because it's before school is out for everyone and the waterfalls are at their highest.
I don't know if you'll have a good time. It will be cold, but I have a good time. Bring warm clothing and hot drinks.
For crossing the Sierra, the main alternate is I-80 around Lake Tahoe. You can also cross year 'round near Isabella Pass south of Bakersfield.