Lush Wine and Spirits just opened an outpost at Chicago and Noble in West Town -- 1412 W. Chicago Ave -- not far from Wicker Park. Will not be a one-stop kind of place and the prices can be on the high side, but a very well-curated selection of liquors (+ beers and wines), if the other stores are any indication.
Binny's has a good selection of most different liquor types, probably the greatest breadth of any liquor store in town (although not necessarily across all categories), including probably 15-20 different ryes, from Old Overholt up to some Hirsch bottling that runs north of $100. I imagine either the Grand Ave. store or the former Sam's location on Marcey St. is closest to you, but each would be a drive.
Not sure Binny's has the best selection of bitters (they certainly have the basics like Peychaud's and Angostura). Consensus amongst those I've spoken to seems to be that Drinks Over Dearborn has the best bricks-and-mortar selection of bitters.
Perhaps others are aware of a good, basic liquor store in the immediate Wicker Park area.
Lush Wine & Spirits1412 West Chicago Avenue
Chicago, IL 60642
312-666-6900
Binny's Beverage Depot213 W. Grand Ave.
Chicago, IL 60654
312-332-0012
1720 N. Marcey St.
Chicago, IL 60614
312-664-4394
Drinks Over Dearborn650 N. Dearborn St. (at Erie), 2nd Floor
Chicago, IL 60654
312-337-9463