Seeing the bulk of New York City's biggest attractions can mean spending a hefty chunk of a trip's budget on tickets. Empire State Building? $20. The Met? $20. The Guggenheim and Whitney go for $18 each. Even the Frick is $15. But there is a lifetime of fun to be had without ever handing over a cent, and not just by taking on park trails, bike paths or window browsing. (Plus some ticket-admission spots have free times too – see the end of the story.)

Free New York travellers, get busy!

1. African Burial Ground
One of Lower Manhattan's most fascinating, and controversial, stories of recent years circulates around the new African Burial Ground National Monument site. It began when a construction project in 1991 uncovered a burial ground of slaves - more than 400 caskets were found - from an age when New York had more slaves than any American city outside Charleston, South Carolina. Outside you can see part of the site now enveloped by buildings, and the compact visitors centre does a masterful job at retelling African-American history in the city. See Lonely Planet's 76-Second Travel Show episode on the museum's opening.

2. Brooklyn Brewery tours
Free Saturday tours of Williamsburg's Brooklyn Brewery run half an hour from 1 pm to 4pm.

3. Central Park
It does not take brilliant travel minds to tell you that a park is free to visit - most parks are. But most parks are not Central Park, Manhattan's famed claim to thinking ahead (even if it was designed in the 1860s to boost real-estate value uptown). It is 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. Another site is "the Pond", at the southeastern corner, where Holden Caulfield kept turning to in "The Catcher in the Rye", wondering where those ducks go when it is cold. (For the answer, watch this video.)

4. Chelsea galleries
New York's most concentrated area for a gallery crawl is in Chelsea, mostly in the 20s streets between 10th and 11th avenues. Check Gallery Guide or for listings. All are free, no pressure to buy. And try timing for wine-and-cheese openings on Thursday evenings.

5. City Hall
Home to New York City's government since 1812, City Hall tours take in its cupola-topped marble hall, the governor's room as well as the spot where Abraham Lincoln's coffin lay in state briefly in 1865. Tours must be reserved in advance.

6. Fashion Institute of Technology (FIT) Museum
It is 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.

7. Federal Hall
Two presidents were inaugurated in New York City, beginning with the first "Dubya", George Washington, who took the oath in Federal Hall in 1789, back when New York was the first capital. (Chester A Arthur was the second.) There is a nice statue outside, overlooking the New York Stock Exchange across Wall Street, and a small, recently renovated museum on post-colonial New York inside.

8. Federal Reserve Bank of New York
Reserve at least a week ahead (sometimes a month!) to visit the Federal Reserve Bank. It is most rewarding just to ogle the facility's high-security vault - useful considering more than 10,000 tons of gold reserves reside here, 80 feet below ground. There are also exhibits on counterfeit currency as well as a serious coin collection of the American Numismatic Society. A tour is the only way to get in.

9. Forbes Collection
The lobby galleries of Forbes magazine have some various curios from the late Malcolm Forbes' collection, most notably early versions of Monopoly boards. (Or watch Lonely Planet's tour of Monopoly sites around the properties' namesakes at Atlantic City, New Jersey.)

10. General Ulysses S Grant National Memorial
Also called "Grant's Tomb", the $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 US, and is patterned after Mausolus' tomb at Halicarnassus, making it a plagiarized version of one of the Seven Wonders of the World.

11. Governor's Island
The ferry to Governor's Island is free, as is access to the 172-acre island which opened to the public only in 2003. There is a 2.2-mile bike path, mini golf, a picnic area, plus military sites such as Admiral's House and a "ghost town" of sorts at Nolan Park.

12. Grand Central Partnership Walking Tours
Two historians lead free 90-minute walking tours at 12:30 pm every Friday, hitting places like Grand Central Terminal's "whispering gallery" and the Chrysler Building.

13. Green-Wood Cemetery
Once the nation's most visited tourist attraction outside Niagara Falls, the gorgeous Green-Wood Cemetery was founded in 1838 and is the eternal home to some 600,000 people (or about 530 miles of bodies, head to toe). It is leafy and lovely, features Brooklyn's highest point at Battle Hill, a site from the Revolutionary War, now marked with a seven-foot statue of the Roman goddess of wisdom, Minerva. Watch for the squawking green parakeets at the cemetery's Gothic entry -- these are runaways from a JFK mishap in 1980 and have lived here since.

14. Hamilton Grange
You know you are important when you get a grange. This one, Hamilton Grange, to reopen in 2011 after renovation, is the Federal-style country retreat where Alexander Hamilton spent quieter, pre-death-by-duel New York days.

15. High Line
It is a park, so it should be free, but the expanding High Line project has the impact and feel of a real-live attraction, complete with its own opening hours. Created from an abandoned stretch of elevated railroad track, the native-inspired landscaping of this park 30 feet in the air connects the Meatpacking District with Chelsea's galleries (another great free institution). There are wonderful Hudson River views, or of pedestrians on the sidewalks below. Watch for public-art installations and events.

16. Hispanic Society of America Museum and Library
The largest collection of Spanish art outside Spain fills the ornate Beaux Arts space of the Hispanic Society of America Museum and Library on the serene Audobon Terrace in far north Manhattan.

17. Japan Society
The films and lectures usually involve a ticket, but the gallery exhibits at the Japan Society (focusing on Japanese art) are always free.

18. National Museum of the American Indian
This Smithsonian ex-pat, just off the historic Bowling Green and Battery Park, often gets missed by the frenetic commuters and tourists heading to the Statue of Liberty. Situated in the spectacular former US Customs House (1907), the National Museum of the American Indian is actually one of the country's finest collections of Native American art. The focus is on culture, not history, and does so with many of its million-plus items.

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

20. New York Public Library
Remember the Dewey Decimal System? The New York Public Library, New York's most famous library (aka the Stephen A Schwarzman Building), which turns 100 in 2011, is situated in a grand Beaux Arts icon east of Times Square. It is fronted by marble lions named "Patience" and "Fortitude", and is just a jaw-dropper to walk through, particularly the reading room fit for 500 patrons reading with the aid of the library's original Carre-and-Hastings lamps. There are exhibits too, including a copy of the original Declaration of Independence, a Gutenburg Bible, plus 431,000 old maps. There are free tours at 11 am and 2 pm Monday to Saturday, 2 pm Sunday.

21. Old Stone House
A Breuckelen legacy from Brooklyn's Dutch origins, and a survivor from the ill-fated Battle of Brooklyn, this Old Stone House features a small exhibit on the battle. Its upstairs is sometimes rented out for the likes of sample sales.

22. Public boathouse kayaking
Kayak for free from public boathouses such as the Downtown Boathouse and Long Island Community Boathouse in Queens.

23. Rockefeller Center Public Art
Built in the 1930s Great Depression, the 22-acre Rockefeller Center is more than the setting for NBC's Today Shows (lines often appear by 6 am) and a giant Christmas tree in December (not to mention to $19 NBC tours or $21 trips to the observatory deck). But do pop by to see the slew of art commissioned under the theme of "Man at the Crossroads Looks Uncertainly But Hopefully at the Future". A bit wordy, but the pieces pack a big punch, such as the statue of Promethus overlooking the skating rink, or Atlas holding the world at 630 Fifth Ave. Jose Maria Sert's murals in the (main) GE Building used the likes of Abe Lincoln to replace the original "communist imagery" (eg Vladimir Lenin) by a snubbed, outraged Diego Rivera.

24. Schomburg Center for Research in Black Culture
Part of the city's library system, the country's largest collection of documents, books, recordings and photographs related to the African-American experience, the Schomburg Center also hosts free exhibits.

25. Socrates Sculpture Park
On the East River, overlooking Roosevelt Island and the Upper East Side, the Socrates Sculpture Park, a former dump site, now has interesting art installations, light shows and movies on Wednesdays in summer.

26. Staten Island Ferry
Everyone wants to see the Statue of Liberty. Ferry tours there start at $12. But the Staten Island Ferry for commuters, cutting across the New York Harbour, is absolutely free and has long held the distinction as the single greatest free attraction on the Eastern Seaboard. Around since 1905, the ferry carries 19 million across the harbour each year. Technically for transport in between Staten Island and Manhattan, most visitors simply hop back on to get back to New York. It never gets old.

Free attractions at scheduled times

27. American Museum of Natural History
Free its last hour (4:45-5:45pm).

28. Brooklyn Botanic Garden
Free Tuesday, and 10 am to noon Saturday.

29. Brooklyn Museum
Free first Saturday of the month, when there is a big wine tasting and DJ parties that draw half the neighbourhood.

30. Bronx Zoo
Pay what you wish on Wednesday.

31. El Museo del Barrio
Free the third Saturday of the month.

32. Isamu Noguchi Garden Museum
Pay what you wish, first Friday of the month.

33. Museum of Modern Art
Entry is free 4pm to 8pm on Friday. Gets busy.

34. Museum of the Moving Image
Free 4 pm to 8 pm Friday.

35. Neue Galerie
Free 6 pm to - 8 pm the first Friday of the month.

36. New York Botanical Garden
Free Wednesday, 10 am to noon Saturday.

37. New York Historical Society
Pay what you wish, 6 pm to 8 pm Friday.

38. South Street Seaport Museum
Free the third Friday of every month.

39. Studio Museum in Harlem
Free on Sunday.

40. Wave Hill
Free 9 am to noon Tuesday and Saturday.

The article 'Forty free attractions in New York City' was published in partnership with Lonely Planet.