This may sound off-the-wall, but consider going up the John Deere Classic in July. You could catch a golf tournament and get in some reasonably priced golf, probably with less humidity than in Florida. Quad Cities Airport handles regional flights.
The tournament is held at Deere Run GC in Silvis, IL, (near Moline) and was originally known as the Quad Cities Open. http://www.johndeereclassic.com/
It's been nicknamed the Midwest Major, and ended up last year in a playoff in which Zach Johnson edged Troy Matteson. The two bumped Steve Stricker out of the limelight - Stricker was trying for his fourth consecutive Deere win. All three golfers, and several others on the leader board, had Illinois or Iowa connections.
Anyway, it's a major tournament, but lots of reasonably priced hotel rooms were available. My wife and I drove up and really had a good time.
Area also has several very nice public and semi-private courses. Very interesting is Arsenal Island Golf Club, on the grounds of the Rock Island Arsenal military base, which is located in the middle of the Mississippi River. Arsenal Island's was built and refined from 1897 through 1906, and has lots of classic design features - including back-to-back par 3s on Nos. 16 and 17. http://www.arsenalislandgolf.com/
Note: Deere Run is a TPC course, but the public can play on a space-available basis. You'd have to contact Deere Run to see when play might be open after the tournament.
Edited by WUTiger - 1/9/13 at 1:08pm