the streets and just people watching.

Our favorite pie place (pizza in NYC is pie) was Patsys, right under the Brooklyn Bridge on the Brooklyn side. Beautiful views of Manhattan near there. This was 25 plus years ago, so may not be there now. There are several Patsys in Google. A and C trains stop right by there. Other trains are close.

Ellis Island is great.
Take a boat that goes to or near the Statue of Liberty, many tourist tours, Ellis Island or Staten Island Ferry all go to or near.
Go to a viewing platform atop one of the tall buildings. Chrysler, Empire State or Rockefeller or others.
Chinatown is cool
Christopher Street has lots of rainbow flags.
St. Patrick's Cathedral
Aquarium
The Temple
Bronx (or Central Park) zoo
Skate at Rockefeller Center
Natural History Museum is awesome
The Met, Guggenheim and many other awesome art at museums.
9/11 memorial
Grand Central
I enjoy public transit. Never felt like I was in danger. We did see several officers literally throwing a guy that looked high around one time.
If you like parades, there is a parade somewhere many weekends, some weekends multiple parades. My 2 favorites are the famous Thanksgiving Parade and Halloween on 6th Ave. Crazy costumes, like costumes that cost thousands or tens of thousands.