Toddlers can find Yellowstone National Park boring; they will usually have a number of problems with the place. Yellowstone is huge and is a long way from anywhere, so the amount of time the child spends strapped into a car seat is challenging at best. Further, the attractions that engage the adults—the geysers, the canyon, etc—do not mean much to little ones. Here are some things that the very small child can enjoy about the place, too.
Understand that the challenge is to find a place where small children can safely blow off steam. The geyser basins are not usually safe places for them—they do not understand how dangerous the boiling water is—but the Old Faithful area has a couple of excellent options.
Try some of the more stroller-friendly parts of Old Faithful (also called the Upper Geyser Basin). You can, for instance, walk the trail that runs northwest along the Firehole River to Morning Glory Pool. This trail is actually the former route of the highway, and is paved.
Toddlers need to run around, though, and a good place to do that is actually indoors. Try the Old Faithful Inn, the big log hotel that is the most prominent building in the area. The lobby is a good place for small children to exercise, and adults will find it impressive, too (be a little more cautious on the upper levels of the lobby, where the balcony rails are not quite toddler-proof).
Go to hotels elsewhere in the park, where similar opportunities present themselves. The Lake Lodge and Lake Hotel, both on Yellowstone Lake, have lobbies where toddlers can take a break, as does the hotel at Mammoth Hot Springs. At Mammoth, you will also find expansive lawns where kids can play without getting too close to the abundant car traffic.
Try playing the “spot the animal” game while in the car. This will work for slightly older children, 4-year-olds, and possibly 3-year-olds. Some of the animals of Yellowstone, like elk and bison, are so big and plentiful that small children will be able to spot and maybe even identify them.