You can never be bored in a city like New York City! The amount of museums and activities and amazing restaurants make this place the city that never sleeps. I spent a great deal of time in Manhattan, as I lived there, and I must say it was a great experience.
If you have never visited, I would suggest staying away staying in the tourist traps like "Times Square". Of course, I do recommend visiting as it is jaw-dropping, albeit tacky, and if you're travelling with kids they will surely get a kick out of it. Instead opt for a boutique hotel in Soho or even as far as a nice hotel in the Village.
When I lived there last summer, I got to go to so many neat places that tourists generally skip over. My favorite restaurant in Manhattan is called L'Esquina. It's a very neat concept because you have to call and make sure you are on a guest list. L'Esquina is located in SOHO and it appears to be a Taco Shop, but if you are on the list a bouncer in a suit will take you through a secret door into an underground fancy mexican restaurant and tequila bar. Its a great place to have dinner!
Also if you are int he mood to go out, a place I love to go to is called "APT". When I first went I was surprised at what I found inside. It is located in the meatpacking district and it has a very nondescript exterior. When I went inside however I saw that the entire club is made to look like someone's apartment, speakeasy style. It was really cool and I love going there.
Of course what trip to New York City would be complete without a trip to Broadway, so be sure to go to at least one show while you are there - they are unlike any theatrical performace you have ever seen before (unless you've been to vegas that is!!)
Hit up the shops - on fifth ave, and in soho where the prices are high but you'll be sure to spot some big name celebs. I always find some of the best shopping right on the street. It's very affordable too! One time I went in to a very expensive store and fell in love with a pair of jeans - but they were 300 dollars. I went outside and on the street a man was selling the same ones for $40. I certainly lucked out - there are deals like that on Canal St. too.
I love every chance I get to visit new york city. Its a big overwhelming, overcrowded, and overexpensive - but totally worth it!!