My top two recommendations are Naha or North Pond. "Superb and lovely" fits both places. Both have outstanding food - which is why both chefs (Carrie Nahabedian and Bruce Sherman, respectively) are James Beard Award winners. Both offer very special experiences, without the super high prices of the top tables in town. (Both have $40ish entrees and generally total in the $100-130 range per person including moderate alcohol and tax/tip.) Naha offers the pampering atmosphere of those super-expensive places (but without the formal attire requirements). North Pond provides its exquisite setting in the middle of the park, facing its namesake pond, with the city skyline looming over the opposite shore.
http://www.naha-chicago.comhttp://www.northpondrestaurant.comA bit less expensive, and within walking distance from the Palmer House, are Vivere (the fine-dining Italian restaurant in the Italian Village complex) and Atwood (contemporary American with the view of passersby outside, in the Hotel Burnham).
http://www.viverechicago.comhttp://www.atwoodcafe.comWherever you go, when making your reservation, let them know it's a big anniversary dinner.