Kids love exploring the Old Town with its maze of well-kept alleys and quaint shops.  For 20 RMB they can ride through town on a pony, which will be a hoot.  The public bathrooms in the Old Town were a shock -- they are so clean you could eat off the floor, and have nice lighting, potted plants and video screens in each stall and urinal.  Most of the restaurants in Lijiang Old Town are very kid friendly and have good favorites like hamburgers, mac & cheese, and the best french fries you'll ever have in China. 

The highlight of any kid's (and adult's) visit is a trip up the Yulong (Jade Dragon) Snow Mountain by cable car.  Reaching an altitude of 4500 m (nearly 15,000 ft), the views of glaciers and the surrounding valley are incomparable.  The kids may not be bothered as much by the thin air as the adults, and they will enjoy playing in the snow and making the hike (by staircase) to the top.