"Founded by the legendary scout and showman, Colonel William F. “Buffalo Bill” Cody, Western attractions such as nightly summer rodeos, gun fight reenactments, cowboy music and the world-class Buffalo Bill Center of the West offer just a few things to do in Cody." About an hour drive to/from Red Lodge, MT.
There are a lot of hot springs in Montana - most are in the western portion of the state, but there are a few within a reasonable driving distance from Red Lodge/Billings. Keep in mind, some are associated with a resort and are developed while the others are a bit more rugged. Yellowstone Hot Springs (https://yellowstonehotspringsmt.com/) Hunters Hot Springs (https://www.ktvq.com/news/local-news/signs-spark-interest-in-revival-of-historic-hunters-hot-springs) Boiling River Hot Springs (https://www.nps.gov/places/000/boiling-river.htm) Chico Hot Springs (https://www.chicohotsprings.com/) **Under new ownership, recent reviews aren't great
Fly Fishing Only Adventures Rocky Fork Outfitters & Guide Service Waters Edge Outfitting Montana Trout Scout LLC Skyline Guest Ranch and Guide Service Greater Yellowstone Fly Fishing Yellowstone Horse and Mule - backcountry fishing Stillwater Anglers Yellowstone Fly Fishing Co. Beartooth Plateau Outfitters LLC
Elk River Outfitters Remington's Alpine Outfitting Barron Ranch Yellowstone Horse & Mule Skyline Guest Ranch Beartooth Plateau Outfitters LLC Paintbrush Adventures
This time of year the rivers will be pretty low - not likely any wild rapids. It can still be a fun float down the river to enjoy some scenery though! The leaves should be changing yellow around then. Also, pretty close to rutting season so possibly more moose/deer/elk on the move. Grizzly bears and black bears are also more active in the fall. Absaroka River Adventures Adventure White Water