A Clean Well Lit Place... to study
It sounds like you're in the Lincoln Park neighborhood, but I studied for the bar exam at Letizia's Natural Bakery on Division. In addition to having excellent sweet treats, it is quiet enough to study in, but still has enough movement when you want to take a break and people watch.
I suggest that you avoid Argo Tea unless you want to purchase something. I frequent the Rush street location near Pearson and it is usually crowded and a little noisy on occasion. Furthermore the wifi is not free and requires a purchase to receive the access card. You are granted two hours of access with purchase.
Given the fact that studying is your primary goal, I'd suggest you venture one block north to ING Direct Cafe. It is large, spacious, has free wifi, coffee/snacks if you desire, and is rarely crowded. Computers are provided at each station, giving you the option to leave yours at home if desired.
21 E Chestnut
Chicago, IL 60611