Dan, assuming you have a vehicle, or access to one, check out VRBOs or local rental agencies in quieter but charming Green Lake, which is a nice drive west from the crowds at Oshkosh. Planes will be flying above the lake all during that week; we did that one weekend by accident a couple of years ago. Also (in addition to the American Club at Kohler), The Osthoff near Elkhart Lake, which has the bonus of being within hearing distance of Road America, and you could check the schedule to see what event is happening that weekend or not. If you're not averse to driving, and you like food and beer, stay in Milwaukee and drive up and back. The Iron Horse or the Pfister for hotel, and anywhere in the Third Ward or Kinnickinnick Street for amazing food.
Luis should chime in, too...