Yosemite National Park is an ambitious day trip from the San Francisco / San Jose area. The maps programs say it is about a four hour drive from where I left in Mount Diablo. If you'd rather not be in the city, the drive is scenic and the park is beautiful.
California Landscape between Oakland and Yosemite
I took this trip in March and it turned out I was lucky. There are times when they close the roads in the Sierra Nevada Mountains to cars that don't have chains on them due to the significant snowfall. One of the roads I took was closed only a couple of weeks before I went.
Sierra Nevada Mountain Road in March
If you are only going to Yosemite for a day, the area I visited near Yosemite Falls and Mirror Lake seems like a good place to start. This means you would take Route 140 into the park towards the Yosemite Valley Visitors Center. Here is a photo to give you an idea of the scale of the mountains.
Yosemite Falls near the Visitors Center
Simply driving in and out of the park you will see some amazing scenery. There are sheer cliffs of granite-grey colored rocks with plenty of evergreens climbing up the bases. There was a lot to take in even just between the falls and Mirror Lake. The falls near the Visitors Center is a good place to return to at Sunset for the dramatic lighting you will get on the falls.
Yosemite National Park Cliffs
Yosemite National Park Scenery
The only other named attraction I saw was Mirror Lake, but I was not disappointed. You can truly get some great photos there. Here is one right-side up and two that are upside-down.
Mirror Lake at Yosemite National Park
"Rocks in the Sky" in Mirror Lake at Yosemite Park
Mirror Lake Reflection (inverted) at Yosemite Park
So, I was pretty happy with the area I visited given only part of an afternoon. I'd recommend leaving very early in the morning and going direct to the park to see more. The next place in the area I would have visited is Glacier Point, but I ran out of daylight (going in June would help). Enjoy!
Remarks: I took this excursion a long time ago while on a business trip. You may see a red line going down the length of the photos. These are scans of 35mm film negatives and it exists on the negatives.
http://kimbriggs.com/photo/california-sites/yosemite