Hi there...you are definitely right that Chicago offers a lot of options in that department. The private dining rooms at Spiaggia are really nice (great view, can customize the menu and options for your budget etc.) and the Little Goat is on the opposite side of the spectrum and much homier but also very cool.
I did a dinner for the out-of-towners for my wedding at Fork which was very nice but 35 might be a bit of stretch with their space. Menu wise it was nice as you had free range of everything.
“There are people in the world so hungry, that God cannot appear to them except in the form of bread.”
― Mahatma Gandhi