Colleen & I were in NYC at Xmas, and one thing I hadn't done in all my visits to the City finally got checked off -- up to the observation deck of the Empire State Bldg. It's kinda been turned into a theme park experience while you're waiting in line inside the building, but they've obviously put some of the large admission fees to use restoring these areas, and reading the history of the building whiles away the wait. When we got out onto the deck, it was serendipitously sunset, and not-so-serendipitously a 30+ MPH wind that you had to lean into to move around the west & south sides. But the scene was fabulous, both before & after the sun left. I stayed up there for about an hour.
Lunch at and browsing through Zabar's (Broadway between 80th & 81st) is a unique experience.
I'll 2nd and 3rd going to Times Square, but only if you do it at night. And I'd say the weekend crowds make it more memorable.
Macy's (34th and Broadway) is freakin' un-be-lieve-a-ble. World's largest store. Escalators (on the upper floors) like I haven't seen since Korvette's in downtown Hartford in the 60's (they're wooden). Departments larger than most stores. Things you didn't even suspect they make for sale. Helpful salespeople!
If you're at Macy's, then Penn Station is only a block away. I like it almost as much as Grand Central.
And...when you are walking, always look up! The buildings -- all of them, not just the famous ones -- have architectural details that are often beautiful, frequently awesome, sometimes puzzling. Yeah, you'll look like a tourist, but that's what you are anyhow and you'll have something the natives don't. This is particularly true in lower Manhattan, where the buildings squish against each other.
If you take the West Side river walk (Hudson River Greenway), near the Freedom Tower, at Vesey St and North End Ave (right next to the Greenway) is something that is surprising and quite moving. It's a tilted area of grass & gorse about 50 by 100 feet comprising the Irish Hunger Memorial. The soil & stones comprising it are from the West of Ireland. I spent a lot of time walking around the base reading the quotes...and upped my charitable giving deduction at work as a result. Even more moving than the Irish Memorial Monument in Philly.
Check out the gardens in Battery Park on your way to & from the Staten Island Ferry.