Not sure what you consider walkable, but Iguana Cafe is reasonably close, reasonably good, and open late. I would consider it walkable, but my wife would likely beg to differ (although her shoes are frequently substantially less comfortable than mine). It is farther from G&G than it is from The Publican. Looks like it's open until 12:30 a.m. Sun through Thurs and until 2:00 a.m. Fri and Sat.
Unfortunately, I think your options for a "pure" coffee house are going to be somewhat constrained in that neighborhood at that time of day.
Iguana Cafe
517 N. Halsted
www.iguanacafe.com