I would definitely start by finding an agent you feel comfortable with. Call several from listings you see and see which one knows their stuff (and works well with you). The word "inexpensive" in NYC terms is hard to define, but there are areas that are less expensive than others (utility costs will be a modest part of the cost, not the determinant of what types of units or areas you should consider). My colleagues advice about the 40-times rule is right on. In general, you can figure what you can afford by taking your total annual household income and dividing by 40 - the result will be what a typical landlord would feel you could afford (you may feel that you want to spend less and again that will determine where you should start looking). In most parts of Manhattan, a two-bedroom apartment will run you anywhere from the $4000 range upwards, I'd say most average 2-BRs in the $5000-$6000 range. Again a good agent can point out units that suit your needs. Good luck in the search! New York's a great place!
Charlie Summers, Bellmarc Realty 917-376-1648