Sorry I was out yesterday. I'd be in for this too. I'm near Thermopolis which is 83 miles south of Cody. Cody is a tourist hell from memorial day to labor day. But as was mentioned before or after that you can run into wintery type weather. I would stay away from shoshoni/boysen unless you are out on the water it's pretty much a wasteland.

Thermopolis may be a good alternative for cody. Despite my obvious bias, it's close enough to drive to cody and isn't quite as packed with tourist, better weather-less wind, plently of hotels, campgrounds etc.