Free kayaking at Brooklyn Bridge park https://brooklynbridgepark.org/series/kayaking/
Washington Square Music Festival is happening all month long https://www.ws-mf.org/event-list
Most of the museums and botanical gardens will have a free or pay what u wish day
Fort Greene park hosts free outdoor movie nights
Chamber music by the water https://www.bargemusic.org
Amateur Astronomers Association is always doing something https://aaa.org/events/category/observing/
NYC Parks always host events, nature walks, classes all for free https://www.nycgovparks.org/parks/prospect-park
Art openings are my #1 thing to do. Follow your fav galleries and artists, go see the shows they're putting on.