I will be in Chicago in early October. I'll have time for two good meals. I've done some research, looked at menus, and read some yelp reviews and have spotted these 4 places:
Which 2 of the 4 should I go to? (I've heard Schwa is difficult to get reservations, so assume that I can manage to get it.)
And by all means, if there's a restaurant not listed that I ought to try that you'd recommend, I'd love to hear about it.
Good comments from Gonzo above. Another question I would ask is whether you're sure you want to go to contemporary American restaurants for four out of four meals. There's a lot more variety to our dining offerings. But perhaps you are a professional and this is your area of expertise. In any case, it's something to think about. (Possible ways to vary the itinerary would be to add contemporary Mexican such as Topolobampo or Frontera Grill; modern Italian such as Piccolo Sogno or Piccolo Sogno Due; tapas such as Mercat a la Planxa; etc.)
As for the places you have mentioned...
Schwa is such a nightmare, between making the reservation and having to scramble when they cancel it at the last minute, that I would not recommend it.
To me, Blackbird is the best of the Paul Kahan restaurants, better than Publican, which I found equally noisy but with inconsistent food. Blackbird also has a nice prix fixe bargain at lunchtime.
TRU is outstanding and consistent, one of our very best fine dining restaurants.
Publican is good, but in a category well below the other three on your list. If you are in town over a weekend you could do a fairly inexpensive brunch there and still get in dinners at two others on your list.
Tru is a great choice. Consistent, reliable and outstanding food and service. It is more of a traditional, formal ambiance so it might be fun to contrast it with something different. While Schwa would fit-the-bill for something different, it can be a challenge for out-of-towners. In addition to the tough time making a reservation, they tend to cancel on short notice (sometimes an hour before your meal) and also have consistency issues (my last meal there was a very weak experience compared to my prior meal). A restaurant that has a similar concept and style, but is far more consistent and a bit more refined is El Ideas. They might already be booked, but check into them and if they look up your alley fire them off an e-mail to see if they can get you a reservation.
I don't think Publican is so much in a category "below" the other options, it's just very different. As a gastropub it is much more informal and inexpensive, but fun with excellent food. I, too, love their brunch.
Tru is probably the most reliable of the best you have listed. It is quiet and classy with excellent food and serve service and is in contention with any of the best restaurants I know of. One of the best food experiences anywhere.
Blackbird is much smaller, perhaps a bit noisier with tables closer together. The food is excellent, but perhaps not quite as inventive as Tru.
Schwa is far and away the most unconventional with kitchen staff taking reservations, serving the FOH and, as noted above, sometimes canceling reservations the day-of the reservation. Many people love it. I had an odd experience there, with 3 or 4 of the first courses in our tasting menu being more sweet than savory. Perhaps chef MIchael Carlson was pushing the envelope, but we didn't love the outcome. Would love to try it again, but Mr. CG is reluctant because of our first experience.
El Ideas is very hot now and small and therefore hard to get into (I know because I've tried!). Everest is in a class with Tru food-wise, but we have had poor service issues there. If you decide on it, request a table by the windows. The view is extraordinary.