One of our favorite hikes in Yosemite is up the Mist Trail, which is one of the ways to get to Half Dome. It’s exhilarating to climb the slippery steps (maybe a little more fun on the way up than on the way down).
We typically hike to the base of Half Dome, look up at the hikers climbing up the cables running up Half Dome, and decide that we’ve gone far enough.
The National Park Service now requires permits to climb the cables. See http://www.yosemitehikes.com for more information