6. Explore the New York Public Library
The Stephen A. Schwarzman Building on Fifth Avenue, guarded by the marble lions Patience and Fortitude, is free to enter. Peek into the magnificent Rose Main Reading Room when it's open to visitors, then relax in Bryant Park behind it.
7. Get lost in Central Park
All 843 acres are free. Walk the Mall under its elm canopy, find Bethesda Fountain and Bow Bridge, and climb to Belvedere Castle. Summer brings free performances, including Shakespeare in the Park, with tickets distributed at no cost (expect lines and check current distribution methods).
8. Free museums and history in Lower Manhattan
The Smithsonian's National Museum of the American Indian, in the grand Alexander Hamilton U.S. Custom House, is free. So is Federal Hall on Wall Street, on the site where George Washington took the oath of office in 1789. Trinity Church's churchyard holds the grave of Alexander Hamilton.
9. Hunt for free and pay-what-you-wish hours
Several major museums offer free or pay-what-you-wish admission at certain times, and some are always free. Policies change, so check each museum's website before you go. Note that the Met's pay-what-you-wish policy applies only to New York State residents and certain students; other visitors pay general admission.