Yes, shooting sports are not well "supported" in northern Illinois, what with the current political climate and suburban sprawl taking up more & more land.
That being said, let me introduce you to the Aurora Sportsmen's Club in Sugar Grove, just north of Route 47 on Bliss Road. It's a private club but you can shoot there anytime you choose (8 AM to sunset weekdays, 9 AM to sunset weekends, unless the range is reserved for a match event) once you become a member.
Membership applications are reviewed once a year from March to May. Shotgun sports, black powder, and archery are also well-supported.
No restrictions on "number of rounds loaded" other than absolutely NO full-auto permitted. 100 yards is the maximum at present, but we're building a new facility out near Waterman (Rts. 30 & 23, 20 minutes farther west) that will go to 600 yards & perhaps even up to 1000.
Every second Sunday of each month, the public is welcome to participate in our rifle & pistol matches as our guests.
The only rule is to bring a valid FOID card & sign the liability release inside the range shed when you arrive. Details can be found on the club website at <http://www.aurorasc.org> Monthly calendar of scheduled events is available there for downloading as a PDF document.
Come on over some Sunday morning & get acquainted with the folks who shoot there.