Sounds like you have a passthru permit, but your main focus is hiking Half Dome. No problem!
First day you hike PAST Little Yosemite Valley to set up camp at Sunrise Creek close to where the Clouds Rest trail meets the trail. This is 7 miles up from the Valley floor, an easy first days hike, or if you feel inspired after you've set up camp, do the Half Dome hike in the early evening that first day.
On your second day you could stay at this same camp site and day hike either or both of Half Dome and Clouds Rest.
Alternatively if you did Half Dome the previous evening you could break camp and set out on an easy, relatively flat hike towards Merced Lake and camp at Echo Valley, Lake Merced or wherever strikes your fancy.
On the third day you head down the pretty trail past Bunell and past LYV and down the mist trail for a total of about 14 miles going down hill.