Airbnb could be a good choice. Will your daughter be taking the train or bus by herself? If it’s snowy, the cta train will move faster than the buses, so situating yourselves near a train stop would be a good idea.
Here are two Airbnb’s in the Gold Coast area:
https://www.airbnb.com/rooms/22156370?location=Chicago%2060611&checkin=&checkout=&adults=1&children=0&infants=0
https://www.airbnb.com/rooms/19825611?location=Chicago%2060611&checkin=&checkout=&adults=1&children=0&infants=0
Another good area for you might be River North, maybe in the funky Marina Towers, the corncob buildings at 300 N. State which have the House of Blues and Tortoise Club (jazz) below. Andy’s Jazz is nearby as well.
The Loop where your daughter will be auditioning has changed for the better. Much safer and more to do, so you could try there as well. Printers Row neighborhood might be good. I don’t know much about those areas though.
The Embassy Suites on State Street often has special deals in February unless a convention is in town. Boutique hotels might be worth checking out. There’s one near me called Hotel Indigo. I don’t think it’s too pricey and it’s close to the Clark and Division cta red line train stop as well as the 22 and 36 buses — the Clark and Broadway buses. The 151 buses are a few more blocks away but they go down Michigan. There are other buses as well.
SpotHero would be good to use for parking.
Fun things to do: Chicago Shakespeare Theater at Navy Pier, Art Institute, Museum of Contemporary Art (near Water Tower Place). The new Aire bath house in River West — for a unique R&R experience. Restaurants all over. Music venues. Exhibits. It just depends what you like and where you are.