The "Inn at Chicago" is a renovated hotel from the 1920's, right off Michigan Ave. I stayed there right before Chirstmas, for the first time, choosing it based solely on price. It was terrific. Location was perfect for showing out-of-town relatives the Big City.
For something a bit funkier, one of my favorites is "The Old Chicago Inn", a B&B in the area around Wrigley Field. Also well-priced.
The big problem in Chicago is what to do with your car if you stay down town. Parking is exorbitant. I occassionally leave my car in a "park-n-ride" lot in a suburb and ride the excellent public transit trains into the loop. If you go to a Jewell super market, you can buy multi-day all-you-can-eat ride pass that is a bargain. Good on all the buses, subways and elevated trains.
-JohnD