As a New Yorker, I would like to add my two cents;
Do NOT try to stay as close to Times Square as posssible. No one but tourists and those who profit from them goes anywhere near Times Square. If you want Friday's, Bubba Gump, or anything else you can find in Orlando, go to Times Square.
Visit the Met. But accept that you will be overwhelmed. But don't go overboard. NY has far too many museums to see in one trip.
Take the Circle Line tour. Beset tip ever.
Fireworks? Take the subway to Coney Island.
"Little Italy" = tourist trap. Only tourists eat there. Instead, go a block south and have great Chinese, Malyasian, and Vietnmese food near the Tombs.
For Italian food, there are many options, none of which are in Times Square or little Italy. My two choices for great traditional Italian (not Italian-American) food (at celebrity chef restaurants at good prices) are Becco on restaurant row in the theater district, and Lupa in the Village.
Go downtown, preferably east. The drinks are phenominally cheap (I have an excell spreadsheet of the happy hours of Manhattan).
My #1 recommendation: do the Broadway walk. Take the 1 rain to the top of Manhattan, and walk down Broadway (13 miles) until you get to Battery Park, stopping for pitstops along the way.
Have drinks at the Algonquin Hotel.
Lunch at very high end restaurants is a tremendous bargain.
Hot dogs: forget dirty water dogs. Either choose Gray's Papaya or Papaya King. No comparison.
Pizza: Don't read Zagat's, don't go to little Italy. In manhattan, its wither John's of Bleeker street, or La Pizza Napoleatana. But the best is Di Fara on J street in Midwood Brooklyn (on the way to Coney Island). Bear in mind that the best pizza in NY requires you to wait on line on the sidewald (for up to an hour) and may runout before you get there.
Momofuku Noodle Bar. I would recommend Momofulu Ko, but no one can seem to get in.