I have spent a lot of time at Northwestern recently (pregnant wife and I also live in the area), so I know a decent amount about the options:
1. Corner Bakery: Decent food, good coffee, seating is not that comfortable, but it is directly across the street (southwest corner). Lines can be long.
2. Au Bon Pain (in the hospital): Avoid if you can. Poor food. Good coffee though. When I was spent a month at Northwestern while my wife was hospitalized for pre-term labor, I actually would go to McDonald's [McClurg across from CBS] for breakfast rather than eat the Au Bon Pain food.
3. West Egg: The absolute worst coffee I have ever had. It is amazing how horrible the coffee is. Food is O.K. Greasy, if that's what you want.
A reasonable option: Get your coffee at Corner Bakery (or Starbucks -- there is one on the far north east side of the hospital) and then walk over to West Egg.
4. Fox and Obel: A favorite. I am in there for breakfast almost every weekend. Great food. Very good coffee. Outstanding pastry. Enjoy one before your cardiologist bars them. Downside: Seating can be limited, but it should not be an issue on a Monday.
5. Tutto Pronto: McClurg and Ontario. A decent Italian deli. Breakfast food is O.K., coffee is very good. Seating inside or outside. It can be a nice place to sit outside. Italian version of greasy spoon.
6. If your spouse (or other significant person) is joining you, and you want to have a great but expensive breakfast, try NoMi.