Grab an inner tube, plop into it, and float down the Yampa River. It isn't very deep. (Note: Activity depends on water levels.) You can start at the east end of town, and laze your way through downtown Steamboat on a summer afternoon before coming out at the west end of town. It takes a couple of hours of mostly floating. There are very few rapids. It's at the "C" hole near the library where all the local kids hang out and play in the rapids.
You'll find raft shops on every corner during the summertime at Steamboat. They'll help you find an inner tube that fits, and help with drop-in and pickup. This is something the locals love to do, too. Try Backdoor Sports (970-879-6249; http://www.backdoorsports.com); Bucking Rainbow Outfitters "High Adventures" (888-810-8747 or 970-879-8747; http://www.buckingrainbow.com), or One Stop Ski Shop (877-754-7474 or 970-879-4754; http://www.onestopskishop.net).