WE were there in 2011. Came south from Glacier and set up camp in the National Forest CG just outside the west entrance. A lot cheaper and a whole lot more privacy than Grizzly or any cg in the park. We dry camp plenty so lack of hookups, other than electric, was no issue for us.
We spent a day in Cody at the museum, which is five museums under one large roof. We saw most of three of the museums, never got to the firearms or native american sections in 5 hours! Rodeo was a hoot. We traveled east on US 20 through WY Nebraska and Iowa just for laughs and giggles. Of course we are retired and had no time limit.