In the middle of Wall Street, this museum looks at how the money goes round, and for the non-economist includes some well explained but dull sections about bond ratings and commodity futures. Far more interesting is the dive into the history of the US – and global – financial system. Particularly fascinating is the story of Alexander Hamilton who basically set it all up, gave away New York being the nation's capital in return for the states backing his plans, then got killed in a duel with the Vice President. See moaf.org.
Billionaire financier J.P. Morgan had a taste for rare books and documents, which he kept in his private library. Morgan's book-lined study with lavishly coffered ceiling is majestic, but the library makes the heart swoon. Walnut book cases climb the walls, and on display are one of three Gutenberg Bibles, letters from former presidents, a 1622 version of Othello and a missive from Galileo. It's a treasure chamber for lovers of the written word. See themorgan.org.
An often-forgotten outlet of the Smithsonian Institution, this museum occupies the former Custom House in Lower Manhattan. It does a curiously poor job of telling native American history, but the collection of artefacts that have been gathered are astounding. There are huge spears from the Yamana tribe in Tierra del Fuego, tailored Apache shirts made out of deer hide, Paiute fish traps and effigy figures from Peru.
Most of the 800,000-strong collection came courtesy of George Gustav Heye, a New Yorker who quit Wall Street to indulge his passion for indigenous Americana. See nmai.si.edu.
Inside a disused Subway station, this museum is all about how the millions of people in New York are kept moving. Save the most time for the section on the construction of the Subway system, a mammoth project that was also incredibly dangerous. There are some fabulous photos of the workers digging the tunnels. There are also some pretty grim tales of deaths and injuries, including one poor guy who was essentially blasted into the air through the East River by the air pressure in a collapsed underwater tunnel. See web.mta.info/mta/museum.
In the late 18th century, the Fraunces Tavern was a relatively classy establishment – it even housed the Departments of Treasury, War and Foreign affairs for a few years before New York lost its status as national capital. You can still eat and drink there, but upstairs it has been turned into a very idiosyncratic museum. It delves into tavern life of the revolutionary era, but mainly indulges in its George Washington obsession. Washington gave a speech to his officers here before resigning his commission and going back to civilian life. There's all manner of posters and portraiture, plus the rather more weird lock of hair and church pew fragment. See frauncestavernmuseum.org.
If it's skyscrapers you want to see, then you just have to step outside and ogle the Manhattan skyline. But this compact museum goes into the stories behind the big beasts, and their evolution over the years. Scale models of some of the shiny new glass towers being built around the world are on display, but it's the race to be tallest in New York that really grips. The top tale is of the rivalry between 40 Wall Street and the Chrysler building. The owners of the latter waited until the rival was finished before putting up an extending spire that secured the title of world's tallest building. skyscraper.org
See also: An art lover's guide to New York's hidden highlights