If you are a park goer then
Yellowstone National Park] is a perfect choice. This Picnic spot is one of favourite places of all Cody, wyoming visitors.
If you are a adventure seeker, then you will definitely enjoy The Buffalo Bill Dam, just very near to the Buffalo Bill museum. You can walk over the dam and watch the deep blue water of the reservoir. There is a lake behind the dam perfect for boaters, anglers and windsurfers.
You said you like to visit museums, so another interesting place I can suggest is Tecumseh's Old West Miniature Village and Museum. It has thousands of miniature figures trace the history of Wyoming and Montana from the 1600s to 1890s. You can vist Cody Firearms Museum as well.
You can even go for a Cody Night Rodeo if you visit in summer.
If you decide to drive then I recommend Cody Trolley Tours.
Hope this helps!