Distance: From the museum, there are two loop options. The Porcelain Basin loop is .5 miles. The Back Basin is 1.5 miles. This slide show is of the Back Basin.
Baby jogger accessibility: Plenty of room for even a double jogger. No obstacles at all.
Cool stuff for kids: The active geysers are fun to look at.
Trail shots: Check out the slide show for more.
Notes: All of the established trails within Yellowstone have detailed trail guides available for a $0.50 donation. I highly recommend them. In addition to detailed maps, the guides have lots of interesting facts about the terrain, and wildlife.