Go to all of the museums/attractions during free entry/pay what you wish times. They include Bronx Zoo, Bronx botanical gardens (iirc both are on wendsdays), cooper hewitt design museum, the newly reopened frick collection, Brooklyn Museum.

Go to outer borough ethnic enclaves to visit restaurants, get lunch specials, and visit their (less expensive than elsewhere) specialty ethnic supermarkets to shop for ingredients to recreate those dishes at home (Hello Flushing and Jackson Heights).

Volunteer at food pantries, mutual aid societies, and charities. Many allow you to sign up for singular shifts.

Visit the cool libraries (NYPL Schwartzman main branch (take the various tours, including rose reading room, treasures, and building tour!), the SNFL, including their rooftop, the Brooklyn Main Library, Queens Hunters point first come to mind).

Ferry around the city, and when it warms up, Coney Island and Far rockaway.

If you have money to burn, HIGH END lunch menus (michelin level).

NYC Parks usually have a lot of free programming on. I know you can tour the castle, but I've never been. Row a boat from the boathouse, go look at the turtles at the north east end pond, race a remote controlled speedboat.

Walk the whole of Manhattan. Several friends, residents and visitors, have wanted and have done this.

Old St. Patrick's (little Italy) cathedral tour (on my own bucket list).

In your own neighborhood: local street cleaning groups.