It may technically be a public park, but the expanding High Line project has the impact and feel of a real-life tourist attraction, complete with its own opening hours of 7am to 7pm. Created from an abandoned stretch of elevated railroad track, the landscaping of this park (which stands 30 feet in the air) connects the Meatpacking District with Chelsea's galleries, ending at the Javits Center on the south side of Hell's Kitchen.

Curated by Bushwick native Joe Ficalora, the Brooklyn Collective is the unofficial graffiti museum that brings together top street artists from all around the world. Spanning multiple buildings and several blocks, the art is all temporary, legal and rivals anything you’ll see in a museum.

It doesn't take brilliant travel minds to tell you that a park is free to visit – most parks are. But most parks aren't Central Park, Manhattan's famed claim to thinking ahead (even if it was designed in the 1860s to boost real-estate value uptown). It's filled with free events, statues, people-watching and sites like Strawberry Fields, an “Imagine” mosaic near the Dakota, where John Lennon was killed in 1980.

The Bronx Museum of the Arts' mission is to promote cross-cultural dialogue and make art accessible for eclectic urban audiences. Founded in 1971, its thousands of pieces of contemporary and 20th-century art span all mediums. A universal free admission policy was implemented to celebrate its 40th anniversary.

With mediums from photography to quilting to weather vanes in its collection, the American Folk Art Museum is devoted to the appreciation and expressions of self-taught artists, spanning all time and place.

It's always Fashion Week in the FIT Museum, which features rotating exhibits by students and a surprisingly interesting and detailed collection of the country's first gallery of fashion, picked from a collection of 50,000 garments dating from the 18th century to present.

New York's most famous library, also known as the Stephen A. Schwarzman Building, is situated in a grand Beaux-Arts icon east of Times Square. Fronted by marble lions named “Patience” and “Fortitude,” it’s a jaw-dropper to walk through – particularly the reading room fit for 500 patrons poring over tomes under the library's original Carrère and Hastings lamps. There are exhibits too, including a copy of the original Declaration of Independence, a Gutenberg Bible, plus 431,000 old maps.

Now for something completely different. The Earth Room, Walter De Maria's 1977 art installation, is a single room filled with 280,000 pounds of dirt, combining the framework of an ordinary office with the scent of a wet forest.

Overlooking Roosevelt Island and the Upper East Side on the East River, the former landfill site turned Socrates Sculpture Park is a playful and free outdoor museum and public park with large-scale interactive sculptures and multimedia art installations. On Wednesdays in the summers are free movie screenings with an emphasis on foreign films, preceded by corresponding music and cultural performances.

Also called “Grant's Tomb”, the imposing $600,000 granite structure that holds the remains of the Civil War hero and 18th president, and his wife Julia, is the largest mausoleum in the USA, inspired by Mausolus' tomb at Halicarnassus, one of the Seven Wonders of the Ancient World.

Situated in the spectacular former Alexander Hamilton U.S. Customs House (1907), the National Museum of the American Indian is one of the country's finest collections of Native American art. The focus of its million-plus items, as well as its programs, is on culture rather than history.

In 1991, construction workers uncovered a burial ground filled more than 400 caskets containing the bodies of enslaved Africans from the 17th and 18th century – an age when New York had more slaves than any American city outside Charleston, South Carolina. Today, visitors can tour the African Burial Ground National Monument site and visit the compact visitors center to learn about African-American history in the city.

You know you've made it when you get a grange (the next level unlocks when a hit Broadway musical is written about your life). Hamilton Grange is the Federal-style country retreat where Alexander Hamilton spent quieter, pre-death-by-duel New York days. You’re able to walk through on your own, but a guided tour is necessary to see the historically furnished rooms. They’re offered three times daily.

Two presidents were inaugurated in New York City. George Washington took the oath in Federal Hall in 1789, back when New York was the first capital, and the site was home to the first Congress, Supreme Court and Executive Branch offices (Chester A. Arthur was the second). There's a nice statue outside, overlooking the New York Stock Exchange across Wall Street and a small museum on post-colonial New York inside, which includes the bible Washington used to swear his oath of office.