I stay at the Palmer house quite regularly. You are a short cab ride, or walk to a lot of great restaurants. For steak I love Keefers. I'm in town next week and will definitely be going there. It's a 15 minute walk, or 5 minute cab ride. As mentioned here The Gage is literally right around the corner. It to is good place, excellent and friendly bartendars. The Wit Hotel, which is 1 block north of Palmer House, has a great roof top bar/rest. Granted November in Chicago gets cold, but they may make it hospitable for cooler weather. Fun place. Lots of places to choose from.
The Gage: excellent gastro pub
Mercat a la Plaxa: possibly the best tapas on town
Russian Tea Time: Upscale Russian the the like
Rhapsody: New American in the Symphony Center building
Short cab rides for Steak and Italian:
David Burkes: Very high end, but considered one of the best for steak.
Spiaggia: Top, very high end, Italian. Spiaggia Cafe is less expensive
Coco Pazzo: nice Italian
Piccolo Sogno: another nice Italian.