Two more suggestions -- if your kids can hike a couple of miles, you can have your own private geyser basin -- the Imperial area, near Fairy Falls:
No boardwalks, no crowds. Just watch where you step! The ground that you sit on can be quite warm -- an odd sensation.
And Boiling River near Mammoth Hot Springs is another easy hike -- bring bathing suits and towels and sturdy sandals. Even if the weather is cold, you can sit in the river where the hot springs flow in -- a natural jacuzzi:
If you'd like a few more ideas, check out our blog:
Yellowstone blog post