If you re going to be coming and going like that, I would strongly recommend that you find a roommate situation. That way, it ll be cheap, and there will be someone there to watch out for your stuff while you re away, and you don t have to make a long-term commitment either, and as a roommate you will probably be able to afford something right in Manhattan, too, so there would be no, or very little, commuting involved, too.Good luck, and the link below is to the Manhattan Roommates/Shares category on CraigsList...
I agree with the other poster, try craigslist and look for either a roommate or a sublet (if you want to live on your own). That s the best way to find a short term (less than a year) apartment without having to worry about credit checks, which you will undoubtedly have to go through if you rent an apartment straight-out. As far as where to live cheapest, what s your budget? That would help, as what is cheap and expensive to you could be totally different to me. I d recommend Brooklyn or Queens if you are trying to save money... Astoria in Queens is nice, very close to midtown Manhattan and has a lot of restaurants and shopping. It s not the cheapest neighborhood, but it s safe and you can find reasonably priced places. There are so many neighborhoods it s hard to go through them all, but if you are looking on craigslist, usually they will list the address or cross streets. You can look on google maps to see how close to the train it is and what neighborhood it is in. Then you can google the neighborhood. The NYTimes online has a lot of good neighborhood profile articles that should give you an idea of what it is like, or you can check wikipedia for neighborhood profiles as well.