Last summer we managed to catch one of the Wednesday morning public guided tours through Fermi Lab -- http://ed.fnal.gov/programs/tours/guided-tours.shtml
Granted, there's no razzle dazzle and you'll probably be disappointed if you're expecting some kind of Star Wars experience, but it's still worthwhile seeing the public areas of the facility as if you actually worked there (see photos). Maybe we were just lucky, but we also managed to get fairly close to the buffalo herds a couple times.
Because of the fixed 10:30 time slot, it leaves your whole afternoon free to do whatever. Since it was close by, we spent the afternoon at Cantigny Park.
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