First thing... leran to spell it correctly... Oshkosh. (There's a brand of men's denim coveralls made in Oshkosh whose motto is Oshkosh b'gosh), but I digress.
When you're there you can say hello to of my long time pilot friends, Les and Dave... not to worry, they seem to be everywhere.
The title to beer city of the midwest is shared between St. Louis, Missouri and Milwaukee... so take one of several free tours of a brewery... it's very interesting, even if you forgo the free small samples.
In Oshkosh, try and find time to go to the Paine Art Center ... a pretty good one.
Ride one of the two ferry boats (S.S. Badger's a good one) across the lake to Michigan for lunch.
Somewhat cheesy (no pun intended) but visit this:
http://oldworldwisconsin.wisconsinhistory.org/
Drive up to Green Bay (not far) and have lunch at the Green Bay Packer's Lambeau Field... pretty good food and then you could take a tour through the museum.
Not into American football? Ok... how about some intense shopping? Go outlet shopping in Johnson Creek or Kenosha.
One more then you're on your own... Check out old time Amish living in Amherst.
All are within an hour of Milwaukee. So's Chicago, by the way.
Again, welcome to the U.S. (Are you a pilot by chance?)