Closest to Lincoln Square, and all very good:
Sola
Magnolia Cafe
Sweets and Savories
North Pond
A bit further, but even better, with food that is so sinfully good that it will be perfect for the occasion:
Oceanique
one sixtyblue
I like Blackbird a lot, but I like these two even better.
Since it's a weekday, Oceanique has a special 3-course tasting menu for $39. Everything they have is superb, from the soups, to the sauces, to the scrumptious desserts. one sixtyblue is equally good but they don't have a weekday special like that.
I also don't particularly like Avec. The food is fine, but I don't like going to a place that doesn't accept reservations, and risking having to wait a while for a table. I also don't like the communal seating.