Staying home with your parents for now, and saving up, is a great idea!
You should have some better options in the areas you mentioned..........although Jersey City can be pricier than you might think, depending on the location.
Have you considered towns like Montclair, S. Orange or Morristown? I know they are a bit more "suburban", but they offer the Mid Town Direct train, and have a younger vibe than some other suburban towns.
Just a thought!
You might also want to consider finding a roommate, which might help keep your portion of the rent under 900. I am sure you could always fnd things to do with any savings you might have!
Good luck - sounds like you're on the right track!
It is most likely that I will remain in New Jersey possibly living in either Hudson or Essex county. I am looking to either move to Jersey City, Harrison, or the Ironbound section of Newark. I was raised around these areas, so I am familiar with the neighborhoods. Also, I am impress with the renovation these cities have gone through over the past 10-15 years. Rent is cheap and I see more positive developments in these cities in the future.
I'm in agreement with Don that I don't believe that you will find a 1 bedroom apartment in Manhattan that includes utilities, no roommate, and is located in a safe area within your price range. I suggest that you contact a few real estate agents that are experienced with rentals in Manhattan by calling some real estate firms there to inquire if they might be able to assist you.
And yes, you are correct to be wary of Craigslist ads as there are many scammers on there after your personal information and money.
Good luck to you!
Prudential Connecticut Realty
There's plenty of information online about how to spot such scams. There are also some threads here on Trulia. For instance, you never send cash or a money order to anyone. Ever. Verify that the scammer (oops--the supposed landlord) actually has the right to rent the apartment. Are they the owner, according to the tax records? And don't just take Joe Smith's word that he's the owner, even if the tax records say the unit is owned by Joe Smith. Ask to see Joe's ID to verify his identity. (Even that's not definitive, since the ID may be fake.)
Ask your parents to help you check out some of the places. But, really: $900 for a decent, safe apartment, no roommate, including utilities, in Manhattan? No way. Sorry about that.