The Metropolitan Museum of Art charges around $30 general admission for adult visitors who aren't New York State/tri-state residents; NY residents (and NJ/CT students) pay what they wish under state law. Hours are Sun–Tue and Thu 10am–5pm, Fri–Sat 10am–9pm, closed Wednesdays. Must-sees include the Egyptian Temple of Dendur, the American Wing's Central Park-facing glass court, and the arms and armor collection.
MoMA charges around $30 adult admission; hours run roughly 10:30am–5:30pm, with Fridays extended to 8:30pm — Friday evenings are free for New York State residents via a reservation-based program. Highlights include Van Gogh's The Starry Night, Warhol's Campbell's Soup Cans, and the sculpture garden.
The American Museum of Natural History charges around $37 for non-NY-resident adults; NY State residents can use a pay-what-you-wish option. Don't miss the Milstein Hall of Ocean Life's blue whale, the dinosaur halls, and the Rose Center for Earth and Space planetarium.
The Guggenheim charges around $30 for adults; the building itself — Frank Lloyd Wright's spiral ramp — is as much the draw as the collection, which centers on early 20th-century European abstraction. For a free option, the Whitney Museum offers free admission Fridays 5–10pm with a reservation, and the Brooklyn Museum runs free "First Saturdays" programming monthly. Prices shift often — confirm current admission on each museum's own site before you go.