Be aware that most hotels in NYC require that you be 21 or older to check in. There are some that are 18+, but you definitely have to look for them.
The cost will depend on a lot of factors that you don't provide.
The hotel cost will depend on where you stay, when you stay, and how many are sharing the room (there is generally a max limit of 4 to a room, and this is enforced).
You don't say where you live or how you're getting there, so we have no idea how much it'll cost you in transportation.
I'd suggest using the subway instead of taxis or uber. That'll save you time and money.
Food costs are generally high in NYC, but there are certainly budget-friendly options. But how much you spend on food will depend on where you eat, and there is a huge range in prices.
Other costs will depend on what you want to do. There are free things to do - Central Park, Times Square, window shopping, the 9/11 Memorial, etc. Other things charge a fee - bus tours, museums, Broadway shows, observation decks, etc. So we can't predict how much you'll need for sightseeing without knowing what you plan to see.
I think you need to plan out the details of this potential trip - when you're going, how many of you would be going, and what you want to do - and then you can look up the costs associated with your activities and get an idea of what it will cost. I'd say you nee at least $1,000, but it could certainly be more than that depending on all these factors.