Yellowstone is a great place to take your family. There is so much to do and see. We only had two days to visit, but a week or more would be better. You can camp there, stay in a nearby town, or procure lodging in the park. The kids will love exploring with you and taking their own photos as well.
We stayed in West Yellowstone the first evening. It's a cool little town very close to the West entrance to the park.
If you're a knitter, be sure to stop by the West Yellowstone Yarn Shop and pick up some bison wool.
Just look at the gorgeous fiber still on on this fellow's back in the heat of summer:
Also, when you are in West Yellowstone there is a walk up ice cream stand the has the best huckleberry ice cream!
The first part of the park that we explored was the Norris Geyser basin, which looks like a lunar landscape:
There are hiking paths so you can wander around. You really must stay on the path, because the water bubbling in the pools is more than boiling (up to 280 degrees Farhenheit/ 138 Celsius) and some of the ground surface is not very solid. In the photo below you can see one of the fumaroles (steam vents).
Here's a close up of one of the tiny thermal pools:
In the lower left of the photo there is a bubbling mini-geyser. That water looked plenty hot!
This is Crackling Lake: I fell in love with the color palette!