This is a great question! Here's a list of places in Wicker Park/Bucktown. The atmosphere varies greatly at these options near Division, Damen and Western El Stops on the Blue Line, but the following have outdoor tables:
upscale patio/recommended food:
Cafe Bolero (Cuban, 2252 N. Western Ave) The mussels come with feta.
* Jane's 1655 W Cortland - great food, metromix claims they have a patio *(but I haven't seen it).
MAS 1670 W Division (Latin-inspired) we've loved every pork and lamb dish we've had here
Recommended food, somewhat-less-upscale outdoor dining:
Irazu (Costa Rican, 1865 N Milwaukee) Great vegetarian burrito. Plastic tables in front.
Handlebar 2311 W North --interesting vegetarian, african stew and fish specials. Beer garden out back.
Cold Comfort Cafe & Deli 2211 W North Avenue -- good breakfast, tables out back
Sultan Market 2057 W. North Ave
http://www.chicagofalafel.com/ (arabic, turkish, middle-eastern) Plastic tables on the side.
Silver Cloud 1700 N Damen
http://www.silvercloudchicago.com/ Comfort food, decent beer selection
Toast 2046 N Damen Avenue -- good breakfast, tables out back
Been, OK food:
Mac's 1801 W Division -- bar food, decent beer selection including a hand pump
Adobo Grill 2005 W Division -- ok upscale mexican. We thought too expensive and moles were a little salty/not as complex as other pricey places
Las Palmas 1835 W North -- ok food, especially with coupon -- we liked the tequila and pineapple-glazed skirt steak over rum-soaked plantains
Smoke Daddy (BBQ) 1804 W. Division (now owned by Dunlay's group -- eeek. previously good, haven't been recently)
Places with outdoor dining that we have not eaten:
Bob San 1805 W Division / Mirai 2020 W Division
Feast 1616 N Damen (very nice looking patio)
Scylla 1953 N Damen (a few tables out front)
Meritage 2118 N Damen (patio seating)
Outside this neighborhood, some of my favorite outdoor options are in Greektown (Athena, Pegasus, Greek Islands).