Most of the best, most appropriate places on the North Shore have already been mentioned, but I'll throw a few more into the mix.
I think it depends partly on whether you're looking only for food, only for atmosphere, or a combination of the two. In terms of food, IMHO three places on the North Shore can knock your socks off with one unbelievably delicious dish after another after another:
Oceanique,
Michael, and the not-yet-mentioned
Chef's Station. All three also have a certain casual, almost mischievous attitude about them, which you may or may not enjoy (I do). OTOH, if you're looking for atmosphere - a place that's a bit more formal in feel, "a nice restaurant that acts like a grown-up" - then I think
Carlos and
Va Pensiero may be more what you're looking for. Both have very good food, too, although they haven't just blown me away the way the previous three have. Same thing with several more casual places: the previously-mentioned
Jilly's Cafe, and the not-yet-mentioned
Jacky's Bistro and the
Stained Glass, all of which are casual and have very good food (without the whimsy of the first three). Throw in
Pete Miller's as well, in the steakhouse genre. There you have nine places to choose from, and really, you can have an excellent, enjoyable meal worthy of your special occasion at
any of them - so don't agonize too much over the choice; just pick one and have a great time.
Regarding the three other places previously mentioned by others... I haven't been to Bank Lane Bistro. I've been to the Tavern in Libertyville; the food is very good, although the publike atmosphere might be odd for a celebration dinner (also, I assumed the "North Shore" designation applies only to towns on Lake Michigan). And I was rather disappointed by my January visit to Quince; I thought the food was just okay, with virtually nothing that made me say "yum" or "wow" the way anything at Chef's Station or Oceanique or Michael would. The desserts at Quince were particularly disappointing in both taste and size.
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