Couple of thoughts from my days in Chicago...

Everest is pricey but well worth it IMHO. One of the best (fancy) meals I've ever eaten. That's a very short ride from Navy Pier--it's above one of the exchanges. Totally high-end, great view, fantastic service.

Ambria is a little further of a cab ride ($8 instead of $4) but closer than the Ashland option listed above. Very classy French restaurant in Lincoln Park.

There are lots of other nice places, but for fancy and quiet, these two are great. Just a quick caution--almost all of the steakhouses like Gibsons, Mortons and others are extremely noisy (although the food is generally great).

Have a great time