New York sells four paid views of itself at broadly similar prices, and they are not interchangeable — they show different cities.
The paid decks
Top of the Rock — 30 Rockefeller Plaza. The best for most people, because it looks at the Empire State Building with Central Park behind it. The Empire State's own deck cannot show you the Empire State.
Empire State Building — the historic one, with the longest queues. The 86th floor is open air, which matters. The 102nd is enclosed and higher.
Edge, Hudson Yards — an outdoor triangular platform that projects from the building, with a glass floor section. West-facing, good at sunset.
Summit One Vanderbilt — mirrored rooms and installations as much as a view. Divisive: some find it the best thing in the city, others an expensive art piece.
The free views
The Staten Island Ferry. Free, around the clock, 25 minutes each way, passing the Statue of Liberty on both legs. The best free view in New York by a wide margin.
You must disembark at Staten Island and re-board, which takes a few minutes.
Brooklyn Bridge, walked from the Brooklyn side toward Manhattan so the skyline is ahead of you. Early morning avoids the crush.
Brooklyn Bridge Park and DUMBO, for the classic bridge-and-skyline photograph.
Roosevelt Island tram, which is public transport on a MetroCard and crosses the East River at height.
The High Line, an elevated park on a disused freight line.
The Statue of Liberty
The island requires a ferry ticket from Battery Park. Crown access is separate, limited, and books months ahead.
The view most photographs show — the statue from the water — costs nothing on the Staten Island Ferry.
Ellis Island is included with the same ferry ticket and the immigration museum there is the better of the two visits.
Museums
The Metropolitan Museum — pay-what-you-wish for New York State residents and students from neighbouring states, fixed price otherwise. Vast; pick two wings.
MoMA, the Whitney, the Guggenheim in its Frank Lloyd Wright spiral.
The American Museum of Natural History.
The 9/11 Memorial is free; the museum charges.
Several museums have free evening hours on specific days, which change — check current policy.
Neighbourhoods, which cost nothing
Central Park, which is larger than most visitors realise and best entered away from the southern corner.
Greenwich Village and the West Village, the one part of Manhattan that escaped the grid.
Chinatown, Little Italy, the Lower East Side.
Harlem, Williamsburg, Astoria, Flushing — where the food is.
Practical
The subway runs 24 hours and is the fastest way anywhere. Contactless tapping works and caps weekly.
Tipping is expected — around 18–20% in restaurants — and menu prices exclude tax.
Walk more than the map suggests. Twenty blocks north to south is roughly a mile; the crosstown blocks are much longer.