Where are the best places for a single female to live in NYC?

I'm considering a move to New York City - single female, mid-20s. Where are the best neighbourhoods for single females (relatively safe, close to transportation, etc.)? Thanks! More details.... I'm from Toronto - forgive me...I've never been to New York City. The only knowledge I have is what I've researched on my own, Google Maps and various TV shows. My potential job will be in a building in Times Square. I know many people take cabs in NYC but that will run a bit, so I want to make sure I won't spend more than two hours on the trains/buses to get to Times Square. My budget: anything under $2000/mo...NO roommate. And no roachfests, either!!! I was looking at some apartments online in Harlem. A lot of them have been renovated. Any single women living there can give me an idea of safety in the area?

Public Comments

1. You can live in TriBeca. It's a nie plce and known for its good restaurants. Especially Tribeca Grill. Tastey food. Almost every celebrity has been there. They also have factories that they changed into lofts. They also have a lot of Caucasians and Italians there. Not as much Black, Hispanic, or Asians. Not to be racists. But it is very multicultral and very safe. From my knowledge there is the 1 and E train that goes through there. At some times, the 2 and 3. Edit: The A and C stop there. I think the J, 4, 5, and 6 stop there to. But I am not entirely sure.
2. On the roof, its the cheapest!!
3. I'd say somewhere around Columbia University. It's a relatively safe neighborhood, and it's busy, yes, but it's easy to get around in the morning, and late at night. It's fairly close to bus stops and train stations.
4. Manhattan
5. My house. Come to me and you'll not regret it. JK Manhattan is pretty safe.
6. east village or upper east side.
7. This is impossible to answer without more information -- whether it's "close to transportation" depends on where you're trying to go. Are you planning to work or study in a particular part of town? And what's your price range?