I not only visited the city - I lived there on tight budget! Food and metrocards will cost you a lot, but if you prepare carefully, you might save lot of money.
I am sure you know how to get cheap flight tickets or free accommodation so I am gonna give you some tips on how to save on sightseeing including museums and events and still enjoy your trip!
Trip to Statue of Liberty and Ellis Island will cost you 24USD and if you want to get inside of Lady Liberty, it will cost you additional 30USD (depending if you are senior, junior etc.)
If you are flying to JFK, you might spot the statue from above and realize how small it actually is. They always show her big head in movies and the skyscrapers in distance behind her, but trust me - you will be disappointed. So why waiting for 2 hours to get on tour and paying for it? Once you stand in Battery Park from where the cruise leaves, you will notice harbor for Staten Island ferry about 100metres away. Staten Island ferry is completely free and there is a beautiful view especially in the evening when the sun goes down behind Lady Liberty.
#2 ANIMAL KINGDOMS
Every borough has at least one zoo, but the most beautiful and biggest is in Bronx. Every wednesday is suggested donation day, meaning you don't have to pay at all. It's totally worth the time going all the way up from Manhattan! Be careful not to get lost, because some parts of Bronx have more dangerous beasts than the zoo itself.
Also, there is a smaller zoo in Staten Island which is free every wednesday after 2PM.
#3 PUBLIC LIBRARY
Many tourists go around without noticing or they just take a picture from outside, which is a shame. This old building hides stunning interior (you might remember it from Sex and the City movie where Carrie was supposed to have her wedding :-). There are exhibitions in the main hall and if you happen to stay in NYC for longer, you can get free library card or get free English lessons (held in all 5 boroughs). Don't forget to take free maps and guides that are provided there.
#4 BRYANT PARK
This small park is located right behind the Public Library and has pleasant atmosphere. Christmas markets are held here as well as fashion weeks or you might even meet NY Rangers hockey players on several charity events. But be aware - to walk around in park at night is not wise and lots of homeless people gather there. Check out calendar of events.
Almost all museums have their own stores, which are free to enter of course and provide you will lots of inspiration. Some museums have even particular time, usually in the evening when admission is free. The Whitney Museum of American Art has pay-what-you-wish every Friday after 6PM, The Jewish Museum is free every Thursday after 5PM, Guggenheim is pay-as-you-wish every Saturday from 5:45PM to 7:45PM, Museum at Fashion Institute of Technology is free everyday as well as National Museum of the American Indian, also Museum of Modern Art every friday between 4PM and 8PM.
If you like art, don't forget to visit SoHo in summer, which is full of street artists from all over the world.
Manhattan gets really hot in the summer so having fun in water is better option than sightseeing. The most famous beaches include Coney Island (not Island but part of Brooklyn), Staten Island beaches or The Hamptons (take a train from Grand Centra Station). I prefer Coney Island as there are lot of other attractions there. Don't forget you can't be topless on beach in the US :-)
#7 CENTRAL PARK
You can't miss it. Central park is almost 3 kilometers long and 800metres wide. It's always full of people who come for sport or relax. You can skate here or just watch a baseball match. You need almost whole day to see all attractions this park has to offer. Summer brings theatre shows for free - in Delacorte theater where even Meryl Streep performed one summer. You have to pick up tickets for evening show in the morning. Apart from lakes or small zoo you might enjoy John Lennon memorial (between West 71st and 74th streets) or queen Cleopatra's obelisk (by the Metropolitan museum). Although Central park has its own security guards - rangers on horses, I would definitely avoid this place at night.
#8 FINANCIAL DISTRICT
I love to watch the contrast of old churches and high skyscrapers in this part of the city. Visit St.Paul's chapel next to Ground Zero with photos of heroes killed at 9/11 and pictures from kids from all around the world. Visit New York Stock Exchange and watch busy traders. Admission is free but limited so you better hurry up and get tickets in the morning. Don't forget to visit City Hall, Wall street, Trinity church (lot of famous people are buried here including founding father Alexander Hamilton) or Fraunces Tavern (George Washington gave farewell to his officers are the end of the Revolution here).
#9 FESTIVALS, CELEBRATIONS AND PARADES
Chinese New Year is celebrated at first full moon after 19th of January in Chinatown, Manhattan. Enjoy St.Patrick's day on 17th of March at 5th Avenue - between 44th and 86th street - is full of Irishmen - bands playing and soldiers marching. Easter parade is held in march on 5th Avenue, Gay Parade is between Washington Square and Christopher street at last Sunday in June and St. Anthony's feast is at Sullivan street in Little Italy every June (Italians know how to party!). Try to make it to Central park at 4th of july for fireworks and concerts. First monday in September is Labour Day which means big celebration on 5th Avenue. Last two weeks of September are celebrated in Little Italy during San Gennaro feast. More celebrations include Columbus Day in October at 5th Avenue, Halloween parade in costumes in Village (6th avenue/14th Street), Traditional New York marathon starting at Verrazano Bridge and ending in Central Park is held on first sunday in November, last thursday in November is Macy's Thanksgiving Day Parade starting at 77th Street by Central park and ending by Herald Square. December is great for visiting Rockefeller's center and it's huge Christmas tree with concerts and celebrities.
#10 OTHER COOL PLACES FREE OF CHARGE
Walk in SoHo, Greenwich village, Chinatown and Little Italy costs nothing (ok maybe damaged shoes) as well as Rockefeller center, Times Square, Broadway, South Street Seaport, St. Patrick's Cathedral, Grand Central station, Washington Square Park, gospel in some of Harlem churches - all attractions for free.
What I wouldn't miss is Empire State Building and UN headquaters - both charge you for tickets. If I figure out hot to get there for free, I will definitely let you know! ;-)
What are your highlights of New York City?