Off the top of my head:
Morseland, 1218 West Morse Avenue
Heartland Cafe, 7000 N Glenwood
Glenwood, 6962 N Glenwood (not technically outside, but I think they have windows that open to the street)
Hop Haus, 7545 N Clark
Gruppo di Amici, 1508 W Jarvis (more restaurant than bar, but some food with your cocktails can't be bad!)
I am drawing a blank if any of the places on Sheridan near Loyola have outdoor seating.
A little further west: Emerald Isle, 2535 W Peterson.
There are multiple options in Andersonville with one of my favorites being the Edgewater, 5600 N Ashland.
[Edited to respond to Kennyz's post]
I have sat outside at the Heartland with drinks, but it's been a few years.
-Mary