I lived in Vermillion (KVMR) for quite a few years, It's a very nice airport if your just looking to fuel up and grab lunch in town. Pay attention to wind because it can really get blowing in the summer and is often a crosswind to the only runway. It's unattended unless the airport manager, Denny, is at his hangar; say hi for me if he's there. for overnights, I don't think there is any hangar space available. There is a crew car, the keys are just left in the terminal with the sign out sheet. Red (Can be kind of slow if you're in a hurry) or Cafe Brule are my two favorite lunch spots.
However, if I was stopping in the area for Oshkosh it would be at Yankton. It's a nice airport with a crosswind runway; I've never been there during Oshkosh week but have heard from many people they really roll out the red carpet for the week.
Paul, if you do end up in Winner say hi to Dave & Tess for me, they own the FBO out there now. They used to be based in Vermillion and are a couple of the nicest people you'll ever meet.