The last time I was in Chicago (decades ago!) I think I slept on the floor of a graduate student's apartment.
Ah, yes. I remember those days well, too, and with fondness.
Coffee not far where you're staying (there are others around the city, of course): Julius Meinl, 211 E Ontario; Intelligentsia, 53 E Randolph (across the street from the don't-miss Chicago Cultural Center); Toni Patisserie, 65 E Washington (also great for lunch and, well, pastries)
Cocktails: In addition to those already mentioned: The Drifter (inside The Green Door Tavern) (live music, so best to call and see if the performer matches your taste); Three Dots and a Dash (tiki bar -- OpenTable reservation highly recommended); Ms. Alex likes to take an afternoon break from shopping at Pops for Champagne;
Brewpub: I live in Beer City USA (really!), so I don't avail myself of the ones in Chicago. However, 3 Floyds, a few miles south of I-80 in Munster, IN, has a cult following and might be worth a diversion if you're so motivated.
"Local specialties": Lots of info and debate (which are not always the same thing) about the best places. Chicago dogs (I suspect that's why you mentioned The Wiener Circle) -- I'm not a fan, so sorry, no further info here; Italian beef (Portillo's and Al's Beef are near you -- however, SeriousEats ranked Bari #1 (W Grand bet. I-94 and Ogden, good subs there, too -- might be a good place to stop on your way to Oak Park; it's easy to get onto 290 from there)
Lunch depends on where you'll be. There are so many, many good choices. Some excellent places that are over your price range for dinner would meet that criterion for lunch, e.g., Naha. What do you have planned for that time of day?
Dinner Re the rest of your list, we've eaten at Avec several times, which says something right there. I was disappointed with Acacia's pricey prix fixe dinner, but had a good hamburger in their lounge. I've never eaten at The Publican (horrors!). Hmm, what would be different and unexpected? How about Tanta (Peruvian, with Japanese/Chinese influences)? Vera (wine bar + tapas in the West Loop)? Ms. Alex is a big fan of Bistronomic. Finally, I know it's Italian, but if the weather is nice, Piccolo Sogno, where Grand, Milwaukee, and Halsted meet, has a wonderful patio on which to enjoy their excellent food and service. They also run Piccolo Sogno Due, in River North.
Here are some of Grant Achatz's favorite places. It would be hard to go wrong with any of them (except Hot Doug's, which is no longer). We've eaten at GT Fish several times, but as you mentioned, you have no shortage of good places in CT.