Bin36 is my favorite restaurant/wine place in the city. It is warm and inviting and the food is good too. Wine choices are excellent of course. We do a lot of their events and have never been disappointed.
A bit more trendy (and snooty, in my opinion) is the Tasting Room at Randolph Wine Cellar - 1415 W. Randolph St. They have a nice wine list, but their prices are ridiculous. Cheese and modest finger type foods are available.
Webster Wine Bar - 1480 W. Webster Ave- is this little cozy wine place, great list, great staff, etc. No real frills, just great wine and knowledgeable people. Some food available.
I vote you visit Bin36 or Webster Wine Bar.