I was around the same age as your kids when I first visited to Yellowstone. It was definitely one of the most memorable vacations of my childhood. Since then, I've been back every few years and I manage to find new highlights every time. For I first time visit, I would try to make these the priorities:
Geysers and hot springs:
Even with everything else the park has to offer, these are the main reason that Yellowstone is a major destination. I like to hit as many of the geyser basins as I can but the upper geyser basin is the one that I consider a must. It's a pretty spread out area that encompasses a couple of larger predictable geysers. The visitor center has predicted eruption windows for them and I highly recommend trying to see Grand Geyser (tallest predictable geyser in the world) though the large prediction window can sometimes mean that you have to wait quite a while. There is nowhere else on earth that you can see anything like it.
You might see some "geyser gazers" around the geyser basins. They will stand out with floppy hats, full day packs, radios and often crazy creek chairs. Gazers are amateur enthusiasts/experts and most of them have been visiting Yellowstone every year for quite a while. If you see a large group waiting near a geyser or rushing off somewhere you might find it worthwhile to see if there's something exciting about to happen.
On my most recent visit last summer I "discovered" that early morning visits to geyser basins are probably the easiest way to see a Brocken Spectre (
http://en.wikipedia.org/wiki/Brocken_spectre) thanks to the high volume of steam in the chill morning air and the low angle of the sun. As a bit of a nerd I thought this was pretty neat but ymmv.
The hikes to Imperial Geyser and Lone Star Geyser are, as mentioned by others, quite nice as well.
Grand Canyon of the Yellowstone:
Uncle Tom's Trail is staircase into the canyon that Papillon mentioned and it is pretty cool. There are nice views from the points along the rim but I'd suggest getting there early in the day both to minimize crowds and to make it easier to spot the fumaroles in the canyon.
While wildlife is often a highlight but can be hard to predict. You will see bison and deer with near certainty and there is a good chance that you'll see some raptors and maybe some bighorn sheep. I've only seen wolves by seeking them out, and then only from through binoculars or a scope. Bears and moose happen but they aren't exactly predictable.
Whatever the case, it's a spectacular area and I hope you and your family have a great time!
My boys will be 9 & 7 at the time and are very competent hikers (both have a couple of 14ers under their belt, but nothing technical). We will, however, also be with my brother and his "flatlander" family who are also active. 
