You are definitely going to want to hike to the top of Upper Yosemite Falls, and no trip to Yosemite is complete without hiking Half Dome.   Buy a water purifier, it's very hard to carry enough water with, especially for Half Dome.  You wouldn't believe the number of people who ran out of water on the way UP to Half Dome, and it's a long ways back.

Both hikes are bit scarey, and use common sense.   Two people died the week before we did Half Dome, they got impatient and went to outside of the cables.   

We didn't do it, but my son did "Clouds Rest" a year after we were there.   It's on the east side of the park and he says it's great.