There is one in St. Charles/Geneva near Rt. 38, but there is no separate area for smaller dogs. I believe a dog was just killed there recently because some man brought his agressive dog in and the guy wouldn't even leave AFTER it happened.
So I wouldn't recommend any dog parks that don't have small areas for small dogs. The next closest ones I know of are near Naperville, but I am not familiar with them. One of the ones near Naperville does have a small dog area.