Mitchell's is a great suggestion. I've looked at their private room adjacent to their main dining room, and it looks like it's the perfect size. I've seen a similar sized private dining room at several other places worth considering, all with very good food too:
Pete Miller's, the steakhouse in Wheeling;
Cooper's Hawk, the wine-focused restaurant in Wheeling; and
Inovasi, the contemporary American restaurant in Lake Bluff. Each has its advantages. I've arranged an annual private party at Pete Miller's and it's been successfully received. Cooper's Hawk is fun because people can try wines in the tasting room before dinner. Inovasi has the best food of the bunch, but is a bit further from Glenview than the others. I think
Stoney River in Deerfield has a similar sized room they can use for private parties too.
One thing I'll caution you on. You need to contact the banquet coordinator at any of these venues to see what kind of arrangements they have. Some places will work things out with you and meet your needs, and others, well... When arranging my private party, I looked at banquet menus on the websites at Pete Miller's and at Wildfire. The one at Wildfire initially
looked a lot less expensive. However, they were very inflexible and they turned out to be a lot MORE expensive; they wanted a contractual minimum which was VERY high per person, and that minimum was based on the number of people the room held, not the exact number of attendees, which kills you further unless you have exactly the number that the room holds. I got the feeling that their banquet coordinator was a Lettuce Entertain You employee who was told a set of rules to follow and didn't really care whether they got the business or not, and I do NOT recommend Wildfire for this reason. By contrast, it turned out that Pete Miller's was very flexible, and we worked out a menu that was a lot less expensive than the one on their website. The banquet coordinator there is Amy Huber, the wife of the owner, and she has been terrific in working with us.
I recommend contacting these places BY PHONE with a specific set of questions. (Limit your on-site visits to one or two places after you have some idea that they can meet your needs from discussions over the phone.) Be prepared for them to ask you what date and time, and what your target budget is. Ask them about room charges and contractual minimums. At our dinner we used a cash bar to keep unlimited alcohol from driving up our costs.
You may find more availability, and less of a problem with minimums, for a Friday night than a Saturday night.
Also be aware that six weeks is very short notice for private party arrangements.