So just to prove that you don't need a wad of cash to enjoy the wonders of the Big Apple I've compiled the perfect day spent in the city that never sleeps, where you won't have to spend a dime (well I mean, you will probably have to find something to eat, unless dumpster diving is your thing). This is less of an itinerary, and more of a pick and choose fun mix of activities which you can use to make up your own perfect (free!) day.
Take a stroll around Central Park
No-one needs to remind you that this is free, but I'm surprised at how many travellers I know overlook just how much there is to see and do in the park. Pick up a map from the visitor's centre and try your best to tick off all of the sculptures (or just get completely lost like I did) or head down to the Bethesda Fountain and see if you're lucky enough to hear some choral wonders from singers within the cloisters.
St Patrick's Cathedral, New York Public Library and Grand Central Station
Within walking distance of one another, these historical gems require no entry fee, and will keep you occupied for hours. Take in one of the exhibitions at the library or try to re-create the scene from Madagascar in Grand Central Station much to the surprise of onlookers (I don't actually recommend this second one...).
The High Line
Find the entrance to the High Line off 34th Street - near Penn Station - and take it all the way down to Chelsea. On this converted railway line you'll be able to not only see the Manhattan streets from an entirely different angle, but you'll also be lucky enough to take in several amazing works of public art.
Staten Island Ferry
Want to see the Statue of Liberty without spending a dime? (Or spending hours in line...) The free Staten Island Ferry leaves from the east end of Battery Park, and not only offers views of the lady herself, but a spectacular view of the Manhattan skyline.
Don't want to spend a fortune on the MET and MOMA? Lucky for you the slew of galleries between 10th and 11th Street (see westchelseaarts.com) are not only free, but you may even stumble upon some free wine and cheese.
Walking over the Brooklyn Bridge may seem like a rather banal past time, but it's a must. You'll not only get to see Manhattan from an entirely different viewpoint, but it's the best way to make it over to Brooklyn without spending a dime.
Explore outside of Manhattan
The biggest mistake some visitors to NYC make is to not explore anything outside of Manhattan. And while it's true that many of the bigger 'must see' attractions are congregated within Manhattan, there are a host of things (many free!) to do in the outer boroughs. Even just strolling along the streets of Queens or Brooklyn make for a nice, quiet afternoon.
Times Square at night
Even if you can't afford to fork out for a Broadway ticket, just spending the night taking in the atmosphere of this famous square is enough to entertain anyone. Added bonus: gobble down free chocolates from both Hershey's World and M&M's World.
Bonus Pick (if you're lucky!)
Free Broadway Tickets
If you're without the cash to buy even a TKTS discount ticket, cancellations can be your best friend. You will generally stand a better chance if you're travelling solo, but I have heard of couples being lucky enough to nab a cancelation. You'll have to be patient, and make sure to have a back up plan for the evening if you can't nab a ticket, but you never know - I saw Newsies for $0 (third row back!) because at 2 minutes to curtain up someone hadn't claimed their ticket!