We have used Cody as a base for visiting the Cody area, particularly the
Buffalo Bill Center Museums. Ticket fees provide two days admission, which is needed to experience all five museums. In addition to the rodeo, a visit to the dam on the Buffalo Bill reservoir is also interesting. Cody is also a good base for a day trip over the Chief Joseph Highway and on to the top of the Beartooth Pass.
I agree with others that Cody is too far away for a base for Yellowstone. Camping inside the Park is best and camping in West Yellowstone is next best.
For Cody, we have used the
Ponderosa Campground. IIRC less than a mile from the museum. For dry camping, we have also used
Buffalo Bill State Park.