The Metropolitan Museum of Art, on the Upper East Side facing Central Park, is the best general art museum in the United States and among the half-dozen best in the world. Its collection spans 5,000 years of art history from every culture and continent — Egyptian antiquities, Greek and Roman sculpture, Islamic arts, European paintings from the medieval period through the 20th century, American art, arms and armour, musical instruments. The scale is genuinely overwhelming.
The suggested admission is pay-what-you-wish for New York residents; visitors pay full price (around $30). Plan at least half a day — most people need a full day. The roof garden (open April–October) has Henry Moore sculptures and views over Central Park. The museum is closed Tuesdays. Book in advance in summer. Don't miss the American Wing's period rooms, the Egyptian Temple of Dendur in its glass enclosure, and whatever is showing in the special exhibitions — the Met's temporary shows are consistently among the most ambitious anywhere.