Welcome to the best city on earth and my home.
Please watch this video in full before partaking in all this city has to offer: https://youtu.be/8LmPBPWHJu4
1) If you plan to see the Statue of Liberty a free and great alternative is to take the Staten island ferry which is free, it won't take you to the island but you will be passing pretty close with some great opportunities to take photos. You can also drink on this ferry. Warning, do not get off on Staten Island.
2) Stay away from any of those characters in time square. The naked women, the naked cowboy, elmo and crew, they are scam artists and will try and rip you off.
3) Interesting NYC Museums include the Frick Gallery, Tenement Museum.
4) Top of the rock > Empire state building for views
5) Don't eat at any restaurant in or very near to time square.
6) We are extremely busy people but also very helpful, do not be afraid to approach a New Yorker if you are lost.
7) There is no reason to go to Staten Island or the Bronx (other than Bronx zoo) Stick to Manhattan, Queens, & Brooklyn
Plenty of other tips but I think this should suffice for now.