Green Bay has some other attractions if you're interested like the shrine of American football, Lambeau Field, home of the Packers. There's also a nice railroad museum. It is about a 1 hour drive each way though.
Closer places can easily be found. Have you considered a private house? Http://www.visitoshkosh.org/eaa-lodging.html has most of the available locations listed. For 2 people, a room rental would probably make sense. That's they way I stayed the past several years. Most homes have air conditioning most dorms lack too.