Food-wise, I think the top three BYOB places right now are Schwa, El Ideas, and Goosefoot, each of which serves tasting menus. All book months in advance, but sometimes have cancellations, so you might have a chance depending on your date. Schwa has been known to cancel on guests same-day (not every day but often enough I wouldn't count on them for a special occasion). El Ideas is a fun, casual, and interactive environment, with delicious and creative food. If you are looking for quiet and romantic, this isn't the spot, but I would encourage you to go on another occasion. Goosefoot is a delightful balance of outstanding food, a pretty space, and warm and professional front of the house service, helmed by the team of Chef Chris Nugent and his wife, Nina. (Given that nxstasy entered his response while I was previewing mine, sounds like we agree this would be our top choice if available.)
Goosefoot
http://www.goosefoot.net2656 W Lawrence Ave. Chicago, IL 60625
773-942-7547
El Ideas
http://www.elideas.com2419 W. 14th Street Chicago, IL 60618
reservations@elideas.comSchwa
http://www.schwarestaurant.com1466 N. Ashland Ave. Chicago, IL 60622
773-252-1466