A great activity in the summer is to hop on a tube and float down the Yampa River through downtown Steamboat.  There are several shops in town that rent tubes and will shuttle you back and forth.  Or you can bring your own tube or purchase one in a local sporting goods store.  For the most part it's a relaxing float, but the occassional mini-rapid keeps it interesting.  Great for young families. Kids 4 or 5 years old should handle it just fine (life-jackets are recommended).

And this isn't just a tourist thing; lots of locals go tubing too!