I can't speak in general around the city, but if my neighborhood is any indication then you'll find it in almost every coffee shop, and some restaurants. Within 2 blocks of my house (near Fullerton and Clark) there are 2 coffee shops that let you use it for free (no purchase necessary), a coffee shop that gives you unlimited access with a purchase, and 2 more that give you 2 hours of access with any purchase. Then there's 2 restaurants and a pub which all offer free access, though you'd have to buy a meal or drink. Of course, there's also Starbucks, who give you access if you have a coffee card with them (which costs money, but the internet is free).
I work from home, but I spend more of my time at the local coffee shops because the internet is almost as good, and I get to drink coffee while I work. Probably my favorite spot for free internet is The Noble Tree. No purchase necessary, good coffee, and the most comfortable venue around. http://nobletree.tumblr.com/