I work in Wood Dale, which is right next to Itasca/Schaumburg area. I'm sure you've already checked out the map on here...
All the closer courses aren't going to be anything special. Any of them. Clark Park is the closest, and isn't terrible (for a nine holer). No clue when it closes.
Madison Meadows is a longer course, that is definitely OK for glowing, down in Lombard. Maybe 20-25 minutes southwest of Itasca in rush hour traffic. It is a longer course, if you like airing some drives out. Lombard Commons is in the same neighborhood, a pitch n putt that is also glow friendly.
Shady Oaks in Streamwood is another longer course, pretty open with a few exceptions. I don't know about glowing there, but I imagine parking on the street on the East side of the course, in a neighborhood, and starting on hole #13 or so. Not sure about any riff raff that hangs out in the park at night though, some parts of Streamwood aren't the best.
Central Park in Oakbrook is a high quality 9er, and we have glowed there before, but it is in a hoity toity park district complex (no smoking, no dogs, no alcohol etc. etc.). I've never been hassled there the few times I've glowed, but I wouldn't be surprised.
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In other words, the courses we glow at are OK, nothing great. The ones we normally don't glow at are OK to decent. You'll have to drive quite a long ways to get somewhere above average. I don't get out as much as I did last year, but I would be happy to show you around any of those courses.