If you work in Lower Manhattan, you can get a practically brand new 1 BD/1 BA apartment in Harrison in a building right next to the PATH train station for around that much (look up Harrison Station apartments). The building has a gym and pool included in rent...and no, I am not a representative of the owner (I do live in Harrison though).
Weehawken would be a good option, as it as Light Rail service, Ferry Service and NYC busses and commuter vans directly to NYC stopping at every other street corner. It would be helpful, however, if you were to share your requirements....i.e. size, timeframe, amenities needed.