Assuming you're flying to New York City from somewhere in North America, you can get pretty cheap flights if you play your cards right. New York City has a lot of free things available, such as visiting parks, visiting Times Square, crossing the Brooklyn Bridge, and window shopping on Fifth Avenue. First, I'll define three types of budgets (tight, average and large) for a couple who decides to stay in New York for a week (7 nights). Even if you're not a regular shopper, the prices in New York are so attractive that you quickly fall into the shopping rush.
The first expense you'll have in New York is the transfer between the airport and your accommodation (JFK, Newark, La Guardia). Many of New York City's museums and galleries are also free (or offer free admission at certain times). Taxis and Uber are available in the city, but thanks to New York's legendary traffic, not only does this usually take much longer, but it will also end up costing you much more. Whether you prefer typical Italian, Indian, Vietnamese, or American food, you'll have no problem finding a good place to eat in New York City.
First of all, I think that for a first visit to New York, buying a Pass is very useful, such as the New York CityPass, since it offers the main sights and attractions in New York. Either way, New York City is a great destination for all types of travelers and is worth visiting at least once in a lifetime.