I live in central NJ and commuted to lower Manhattan to work on the World Trade Center restoration, I mention that because other wise I would not have done the commute. When I worked Mid Town my commute by NJTransit was optimally about an hour (I live near Hamilton Train Station, just south of Princeton) . Downtown took an hour and half or on bad days two hours. The difference was one train and a two block walk versus NJTransit train, Path ttrain and a mile walk. One missed connection and the day sucked.
Board in Central NJ is somewhere between $650 and $2000 depending on what you want. Rent for you may be between 1500 and 2500. Commuting is going to be about 500.
The message is that it takes careful planning to make it doable, but on that salary you may be living check to check.