First of all, reasonable *driving* distance? No. What you need is reasonable *train* commuting distance. [Among other considerations, if you re asking this question, you can t afford to park in Manhattan.] Try a budget of $1200/mo. You can probably find something nice in southern Brooklyn, in Queens, or in Hoboken/Jersey City, New Jersey.If you need cheaper than that, you can go farther afield, e.g. to New Jersey suburban towns or Westchester County or the Bronx.
In Manhattan - 1,400 to 5,000.Lower in the outer boroughs. Best bet? Find some areas that you might like that are safe and walk around them to see for yourself. Narrow it down and either look for a building you like or go to a realty office. From there you might get an apartment that is cheaper than what you might see in ads. Sometimes the Super can help, sometimes you HAVE to go through a realty office.
if you have trouble in booking the cheapest hotel, i may help!