If you're not averse to traveling up to Evanston, four of the very best restaurants there are Wine Spectator award winners, and all four have frequent wine dinners:
Oceanique, in particular, has phenomenal food that will knock your socks off and has a wine dinner the last Wednesday of every month.
Another idea, although this will cost you more, is to get a tasting menu with the wine pairings. That way you can taste several different dishes with wines especially chosen to be served with them.
Some obvious examples are Trotters, Alinea, Avenues - but that will run you $300-400 per person. If that fits your budget than go for it.
Many other mid-to-high end restaurants also to this. A few places to consider that will be less expensive:
160 Blue ( the terrance brennan menu)
Sweets and Savories
I am sure that you could find more.
Personally, I've always been adverse to paying big $$ for wine in restaurants since its usually just a product you can get elsewhere with an enormous mark-up. The wine pairings always strikes me as a more interesting wine experience.
A lot of restaurants have great wine lists. Many of those hold wine dinners regularly. And most of those wine dinners are shown in the "events" section of the restaurants' websites.
To zero in on restaurants with great wine lists, a good place to start is Wine Spectator Magazine. They have given their Award of Excellence to 94 restaurants in Illinois, and you can see the list of the 52 in the city of Chicago here:
Click on the column headings to sort by restaurant name or award.
You can use a web search engine to find the websites for most of the award-winning restaurants, and then check to see which of them show wine dinners on the website (quite a few do).
Glancing over the list, some of these (Gibson's, Morton's, Saloon) are steakhouses (which may or may not be what you're looking for); some of them (One Sixty Blue, Kevin, mk, Meritage) are among the best "casual fine dining" places in town; and some of them are among the best for a particular kind of food (Bistro 110 or Cafe Matou for French bistro, Coco Pazzo and Trattoria 10 for Italian, Frontera/Topolo and Salpicon for Mexican, Shaw's for seafood). The list includes the previously-mentioned Meritage and Vinci.
Vinci's has great wine dinners monthly...the one this month is tomorrow night. Menu is posted on line to give you an idea: vincichicago.com
They are so reasonable and always accomodating if there is something you don't like. Such a bargain for all the food, let alone the addition of wine!!