I suggest you consider one of the hop-on hop-off bus tours. They are reasonably priced and stop at all the major attractions in Manhattan, Brooklyn and Harlem. Besides the guided tour you can hop off at any of the stops and spend time exploring. If you buy a two or three day pass, you can use any of the 3-5 routes and treat it like a cab.
Big Bus:
http://www.bigbustours.com/en/new-york/new-york-bus-tours/
Grey Line:
http://www.grayline.com/things-to-do/united-states/new-york-city/#
City Sightseeing
https://www.citysightseeingnewyork.com/nyc-bus-tours.html
I'm a huge NYC fan and have been many times. The worthwhile site list is 100s long and would depend heavily on your interests:
- 9/11 site, museum, WTC
- Empire state Building Observation level (many people actually prefer the Rockefeller Observation floor - top of the rock)
- Central park, specifically the John Lennon memorial (Strawberry Fields)
- Canal Road to shop for the knock-offs <-- this is a hell of an experience, ask to see the "secret" rooms
- Chinatown
- SoHo / Little Italy
- Brooklyn Bridge
- Wall Street
- Statue of Liberty
- Take the ferry to Staten Island from South Street Seaport (passes the Statue of Liberty)
- UN building
- Times Square / Theater District
- Radio City
- 5th Avenue and Park Avenue shopping areas
- Battery Park
- Grand Central Station
- High Line
- Trump Tower / Trump Central Park / Waldorf Astoria
- Trinity Church
- St. Patrick's Cathedral
- Lincoln Center
- Apollo Theater in Harlem
- Greenwich Village
- Seeing Manhattan from Brooklyn at night is mandatory!
There is also a bus tour for all the famous TV and movie sites which is pretty interesting. It willl also point out where many stara are currently living
Museums
Madame Tussauds
American Museum of Natural History
Gugginheim
Metropolitan Museum of Art
Museum of Modern Art
Intrepid Sea, Air and Space Museum (especially if you are a military buff)
If you want a deal on a Broadway show consider;
https://www.tdf.org/nyc/7/TKTS-ticket-booths
Food:
Russ & Daughters
Shake Shack
Hala Guys
Junior's Cheesecake
Doughnut Plant
Spotted Pig
John’s Pizzeria
Nathan’s Famous
Katz's Deli
Iconic Stores:
FAO Schwartz <-- You gotta go here, especially if you have kids. Get a picture with the doormen
Macys
Bloomingdales
Harlem Market
Have a GREAT time Silverbone, NYC is truly an amazing place to visit. If you are considering San Francisco, I have another list for you.