New York has many cheap options in which to arrive from. At my time of travel, I was in Toronto so boarded a greyhound bus which took 5 hours including border control. You can now get cheap flights from the UK and Europe for as cheap as £90 each way if booked in advanced. If based in the Caribbean a cheap flight would be from Puerto Rico as it is classed as internal. Due to the location of my hostel I had to get the subway every day to Manhattan which is cheap but once there I walked everywhere. This is a really cheap way of seeing New York but also good for fitness.
Accommodation – Finding accommodation which was cheap and good value was a little tricky when finding hostels and booking at quick notice. In the end, I plumped for the Westway Hotel and Hostel which is on the Astoria Boulevard North and about a 20 minute walk to Astoria metro stations then another 10 mins on the metro to Manhattan. A 4-bed dorm would cost you about $20-$25 a night depending on the season. They were very spacious, clean and provided you with a great bathroom.
Activities – On the cheap
The New York High Line on West 34th Street between 10th and 12th Avenue is a free 1.45-mile-long walk which takes you through the buildings at an elevated level and provides you with great views. A fantastic activity to get the heart pumping and to grab an ice cream en route in the sunshine.
The Statue of Liberty is a very cheap activity for a morning/afternoon and you can book it for £15 online and get a pass for the ferry there and back, Statue of Liberty and Ellis Island. Plenty of time to get some photos and to walk around the various sights. For a further cheaper option, you could walk it from Central Park to Battery Park but that is about 10km.
Central Park is a massive place to spend your day walking around, lazing about, listening to music, going for a run or hanging with friends. I used to get the metro to Central Park then base my day from there and walk to my next place then back again. Other sights to see would be Wall Street which is the centre of the financial district in the USA as well the Charging Bull nearby. Times Square is a short walk from Central Park and definitely worth going to get the photos and see the lights.
The New York Science Museum is a great museum to rival one you have been to before. General admission is normally $16 for adults but if you get there for 2-5pm on a Friday or 10-11am on a Sunday then it is free. A fantastic way to learn about science about everything you can think of imaginable.
For the best view in Manhattan and to get that classic view you will have to pay $34 to get to the Observation Deck at the top of Rockefeller Centre but it is worth it. I had a few days sightseeing for free to even the budget out. I went at sunset and the views were spectacular but expect queues and delays.
The US Dollar is about $1.4 to £1 and you can access money through any ATM in the many banks around Manhattan.
Food and drink
Due to budget I restricted myself to cheap options that I found walking around 7th/8th Avenue in Manhattan and sometimes I cooked my own dinner. I used to get a deli sandwich during my walk to the metro station in the morning and this would cost around $3 and it was enough to see me through the afternoon. I found a Chinese buffet in Times Square and the general consensus was $15 for all you can eat and drink restaurants.