The trailhead sign states 8.2 miles to Half Dome, but I think that's via the Mist Trail to Nevada Falls and then the John Muir Trail the rest of the way. If you take the John Muir Trail the entire way, I believe it is an extra mile both up and down. (I think it's about another half mile from the Wilderness Parking Lot to the trailhead.)
Usually, when I do Half Dome, I go up the Mist Trail to Nevada Falls in the morning and come back down the John Muir trail in the afternoon from Nevada Falls. That extra mile is quite a bit flatter than coming down the Mist Trail at the end of the day when your legs, knees, and ankles are burning. And much safer in my opinion. The Mist Trail, as it leaves the top of Vernal Falls, can be a little tricky, especially if you don't like walking along a wet granite trail without any guard rails in some places. The John Muir trail from Nevada Falls to the Vernal Falls Bridge consists of ___ switchbacks that are medium in length, but not real steep. I didn't list the # of switchbacks, because some people hate knowing how many they have left. I like knowing because I know when I am getting close to the end! If you want to know how many there are, let me know.
The Mist Trail from the Vernal Falls bridge to the top of Vernal Falls is much shorter, but you will usually get very wet as you go up. If it's cold in the mornings, that's not much fun. Having a rain jacket will make the trip up a little nicer. People who don't mind a very steep grade to the top of Vernal Falls usually take this route and save the extra mile. The older I get, the more I like the longer, flatter trail. Both take you to the top of Nevada Falls from the Valley, and then the JMT takes you most of the way to Half Dome except for a small spur trail to the top.
I'll never do the Seven Summits and I wasn't sure I had it in me to even do Half Dome the first time I did it. But once you do it, you will never forget getting to the top. I've seen a 75 year old couple from Japan at the top who didn't even look like they'd worked up a good sweat and I've seen teenagers who gave up at the Vernal Falls Bridge. You just never know until you do it. Normally, you want to be heading down by 3pm or 4pm at the latest, so that you aren't hiking down in the dark. Take flashlights just in case.
Depending on how much time you have, I always find the 3.2 mile hike to the top of Yosemite Falls to be a great hike. It is overall more steep than the hike to Half Dome, but 5 fewer miles each way. (The top of Yosemite Falls is about 2700 feet in elevation gain at 3.2 miles in length while Half Dome is 5000 feet in elevation gain at 8.2 miles. So YF always seems more steep to me.) The views from the top of Yosemite Falls are great. If you go up there, try to go across the bridge an extra mile to Yosemite Point and the overlook to Lost Arrow Spire. tp://www.mountainsport.dk/yosem1sc.gif.
About half way up the Yosemite Falls trail, you will walk alongside where the Upper, Middle, and Lower Falls come together. Quite a site there too.
Back to the Half Dome Hike. If you like longer, flatter (and drier) switchbacks, I would go the JMT the entire way. If you want to get there more quickly and don't mind some wet, steeper grades with less distance, then you want to take the Mist Trail to Nevada Falls. From there it's the JMT the rest of the way to the top. There is a restroom at the junction of the JMT and the Mist Trail near Nevada Falls. There is another one in Little Yosemite Valley, but a little off the main trail.
The REAL fun of the Half Dome hike is the last mile, or so, to the top. You have to experience it, because it's hard to explain to someone who hasn't done it. You'll see what I mean when you get there.
Bill