The majority of the time your budget narrows down your options for you. . To get even simpler, the first option that is hoped for in many cases is to live in Manhattan, and many people can barely afford to live below 96th street. If you can barely afford to live in Manhattan , you wont have many options, so that help narrow down your options a great deal. That being said, be realistic about what you can afford, once you have educated yourself about different price/neighborhood options.
If you can not afford to live in Manhattan, there are many good options that are about a third less in price than the same space in Manhattan. and a reasonable commute to the city, if that is where you are working or attending school..
Determine your logistical/commuting needs, and find a great neighborhood along the A , E or one of the other express trains. There are many options here, . but the first question that most people have these days is if they even have the option to live in Manhattan. below 96th street. More people are considering Washington Heights/Inwood , for this reason , as the apartments are spacious, and affordable.
There are also some great neighborhoods in Queens, that are very affordable, as Brooklyn has become pricey in the last few years. I hope this is useful information, and wish you the best,