One option to stay in New York are the hostels, the latter being definitely one of the best ways to experience the place. In many cases the fares are very reasonable, although this trend have been some cheap “luxury” high prices they charge per night.
In this case I will talk about cheap hostels in New York, where they can get very comfortable rooms with unique decoration. Sometimes the bathrooms are shared resulting in lower prices, but you can also get rooms with private bathroom for a small additional cost (ideal for that privacy is very important) before entering so you always have to check this option.
As for breakfast, there is a fairly wide range of options to choose from. Some hostels offer breakfasts (even with homemade ingredients), while others simply offer a simple continental-style breakfast.
In big cities like New York, breakfast is excluded in some cases - since each step in the city we have millions of choices to get to try something good to buy, so this is another option to keep in mind when choosing a hostel.
These types of places are usually operated by individuals or couples who enjoy accommodate people around the world (unlike the big chains). Usually the hosts are people very bearable and even fun, so it can become a sort of tour guide of the city, telling us where we go, where we can eat and where we can have fun.
Whatever the case, must be prepared for an experience that is truly personal, as it should be borne in mind that most of the hostels are places that are shared like a house guest: the climate of camaraderie and good ideal bias. You certainly have a very special experience when staying in a hostel, and even who you say you make friends.