The happy hour at McCormick & Schmick's is a good suggestion. Conveniently, a new branch is set to open Saturday, July 8 about a block from the Hyatt. My understanding is that the menu will be much the same and the happy hour will be offered weekdays from 3:30 to 6 (but check to be sure!).
Also in the immediate vicinity is the newest Morton’s, The Steakhouse. They have a discounted bar menu weekdays from 4 to 6:30 and 9:30 to 11. Although I haven’t yet been to either of these new places, I would expect both to be an excellent value (with the discount, that is).
McCormick & Schmick's
1 E Wacker
Chicago
312-923-7226
Morton's
65 E Wacker
Chicago
312-201-0410