11 Madison Park is my first choice. Definitely. It's a nine to 12 course meal. The waiters are so attentive and everything is so detailed. They explain all the ingredients to you when they "present" your dishes. I always feel like a judge on Iron Chef whenever I go there. The waiters put a dome over my dish when I go to the powder room. It still cracks me up a bit. Their mashed potatoes are heavenly (I know, it's a poor man's food but they make it so well!). You also get a take home gift (I've taken cookies and brioche home before). A driver for the company my bf works for recommended it when we asked where he often takes the employees for meals.
Jean Georges is another place to visit (it's up near Columbus Circle). It's a fancy place like 11 Madison Park but their food is overall delicious. It's also right next to Central Park (and close to Fifth Ave shopping!). You can go to Thomas Keller's Bouchon Bakery for desserts at the Time Warner Center across the street. Their cookies are amazing. Landmarc is in the same building. I go for the view, their homemade taffy (I always ask for extras), and their moules frites (you can choose from half a dozen sauces).
Dinosaur BBQ is good but it's in a more grungy part of the UWS (or rather, Morningside Heights/Manhattanville). Don't let that deter you. Their ribs are delicious.
We go to Pearls (on Cornelia, right near all the good shopping!) for oysters. I recommend the baked oysters with cheese on top.
You can also try Park Avenue Summer (or maybe Park Avenue Autumn by the time you come). The restaurant changes their menu and decor with the seasons (hence the name changes). The waitstaff is not as attentive as 11 Madison Park but then the price is much lower. I love their desserts here. They are such works of art.