What part of the city will you be in?
If you're in the "Mag Mile" stretch of North Michigan Avenue, I like the Lobby at the Peninsula Hotel, one of the top luxury hotels in town. The Lobby is a combination bar and restaurant, on the fifth floor, alongside the front desk of the hotel. The room is huge but very spacious, not noisy; it has high ceilings with huge windows along one side. I've been there for drinks as well as to eat, and it's the kind of place you're asking for.
You don't say how old your mom is so I'm going to assume she's not 85 and decrepit, but still young enough to chat over a couple of chocolate martinis. I'm the mother of adult children and while,I'm not a barhound, I certainly agree with the Penninsula. Along the same line, I would suggest the lobby bar at the Ritz Carlton. But they're both pretty sedate.
A little more fun would be Pops on State. I also love most of the winebars in the city to varying degrees, including Bin 36, the Tasting Room and Cru. LeBar on Chestnut makes a pretty mean martini and there's Rebar in the new Trump building, Leg Room on Division and Zebra on State.
Almost forgot. I love Le Bar in the Sofitel on Chestnut and they have great martinis.
These are all pretty centrally located , but it all depends on what kinds of things your mom would like and how quiet you think it should be.