Depending on your price range, our favorites are:
Sushi Samba - My 14 year old would live at Sushi Samba if she could. It's a fantastic Brazilian/Japanese fusion with great drinks. If I could eat their beef maki every day, I would. Try their brunch on Sunday, it's incredible!
One if By Land, Two if By Sea - pretty pricey, but it's a special treat (and a 3 - 4 hr meal)
La Bonne Soup - Our favorite for after a cold walk
Mesa Grill - Do this for dessert. I've yet to be really happy with the entrees there, but dessert? Oooh, now we're talking.
If you're into something different, try
Abyssinia for traditional Ethopian fare. Sitting at the woven tables was a lot of fun (one of our friends is over 6'4" and all of that seems to be legs).
The
Olympic Flame is great for breakfast. Even my husband has yet to finish a meal there, the plates are huge.
ESB: To go up to the observatory alone, it's $20 per person for adults. We just took DD last month. I hadn't realized she'd NEVER been up there!
For later in the year (because I'm a wimp who hates cold on the water): Ellis Island, the Statue of Liberty (though as a Jersey girl, I'm going to have to remind everyone that She stands in NJ waters

)
South Street Seaport
Wander Little Italy and Chinatown. Pop into Pearl River, lots of fun things to buy.
And, of course...
.
.
.
there's always the
Museum of Sex 
ETA: And stay far, far away from
Tad's Steaks, though DH and his coworkers eat there a lot when they're working. Eeewwww. Grease on a paper plate.