. Don't stay in Times Square, it's too noisy and too crowded but nearby is fine.

I preferred the Top of the Rock https://www.rockefellercenter.com/ to the Empire State Building, but if you do want to go to the top of the ESB in high season buy tickets on the internet beforehand so you won't have to get in a long queue. www.esbnyc.com/

Hop on Hop off Bus is a great way to see the city and get your bearings. I think there is a one day and a two day ticket.

Ride the Staten Island Ferry it's free and you get a good view of the Statue of Liberty or get a boat to the Statue. Ellis Island where the immigrants took their first steps on US soil is worth a visit.

Walk across the Brooklyn Bridge, stroll round Central Park and take a walk across The High Line.
If Museums and Art are your thing there is the Met, MOMA and The Guggenheim to name a few.

Do have a walk round Grand Central Station. Have a look round Macys.

Visit the Freedom Tower 9/11 memorial.

Eat some New York Cheesecake and buy a Pastrami Sandwich from a Deli.

The list is endless. Take some comfortable shoes and Enjoy.