I'm a fifth-generation SFer (now in Alaska) who's been up Half Dome 15 or so times in all of the summer months. Grandparents on both side and all the aunts and uncles made many Yosemite trips since the 1920's.
I wasn't able to go up last year in early June because of all the snowpack you got in 2010-11. From what I've heard, so far, 2011-12 is well above average as well. That's going to help your eletric rates, but delay the start of your high-Sierra hiking season. SO I WOULD NOT PLAN ON JUNE this coming summer. Even late June could have snow at 7500' under the Jefferies and it is surprisingly easy to step off the trail and lose time in a hundred yard patch of snow.
A poster above said wilderness permits depend on the trailhead used. True enough. And NOT starting from Yosemite Valley isn't as impacted. But the separate permits for Half Dome are separate and have been changing every year. Make you sure you understand the HD permit procedure – they are all gone within a few hour of going on line. They MAY be a separate catagory for BPer who pass by (e.g. come up the JMT), but I'm pretty sure they limit the LYV overnighters to the same pool of HD permits as the dayhikers.
Personally, I prefer it as a dayhike than schlepping overnight gear to LYV, listening to people yell at bears all night, and then having to carry more stuff down the Mist Trail afterwards.
My REALLY BIG Half Dome advice is START EARLY! 7 am is okay. 7 am hiking away from the Trailhead! 6 am is better. If you can swing 5 am and bring a small light to hike with, better yet. You beat the heat of the day, you do the climbing in cooler, less sunny conditions, you beat the crowds, the cables aren't crowded, you have options if you're going slow, etc. Sometimes I start the Half Dome hike at 5 am and still have the time and energy on the return to bop over to Glacier Point and back, although that does make for a pretty high-mileage and many vertical feet in a day.
Here are my times from September 16, 2010. I was solo on that trip and started way before sunrise.
Happy Isles: 1:58 am
Top of Vernal: 2:34
Junction to top of Nevada: 3:11
Leave LYV: 3:38
Clouds Rest Junction: 4:15
Spring: 4:25 (get water here!!!)
Bottom of sub dome stairs: 5:01
Bottom of Cables: 5:23
Top of Cables: 5:37 am
Total up time: 3 hours, 39 minutes but it dark almost the whole way and I'd done Half Dome the day before with a large group, so I'd have been a little quicker if fresh and starting just before dawn. But I hike continuously at 3.5 mph, and if I need water or food or sunscreen or clothes, I do it as I hike.
Saw the sun rise while on top.
Down time: 2 hours, 53 minutes. Happy Isles at 9:12 am, drove back to lodge and had a rather large breakfast in the cafeteria.
Average hiker times would be 5 hours up and 4.5 hours down.
It's a totally kick-a$$ trip. I find it less trying than a Rim-River-Rim dayhike in GCNP even though the total miles and feet and altitude are a bit less in GCNP. But HD has a nice variety of trail conditions and slope so I don't get so sore doing the same pace all the way up and down and there's not the heat to contend with on HD IF YOU GET AN EARLY START.
You say you and your wife (without kids?) How about after Labor Day to dodge the families and college students? You still need the permits and the days are shorter, but afternoon thunder storms are less likely and the lodging ought to be easier to reserve.
I'm bringing the family (including the 11 year old up Half Dome) in mid August but that's because we're in CA for a family gathering then. But July 1 to September 20 is fine. Normally late June would be fine. Probably fine till September 30, but you never know when winter comes to the high country.