One of my favourite parts of our whole trip was our hike in Yosemite! I wish we had been able to do the half dome but you need a permit for that one and I did not get ahead of things enough. Also half dome takes about 9-12 hours so it's best if you're staying right in the park. 
We decided to go with the mist trail, checking out vernal and nevada falls. It was a very very beautiful hike and not too strenuous. It's just over 10km and the elevation gain is 668m I believe. So some of it is quite steep, which was fun. 
It only took us about 4.5 hours and was lots of fun, but best to get there nice and early. The crowds are intense, and it gets quite hot there in the summertime. We started the hike at 730 am, it was nice and cool and significantly less people on the trail. 

 View of part of the mist trail from the top. 
 Headstand, because why not?