Assuming you pay $200/month in healthcare, ~$1800 a month to max out your 401k, your take home pay is about $5,000 after taxes. In Manhattan and the expensive parts of Brooklyn, your own place is realistically a minimum of $2,500, possibly as much as $3,000. Outside of those places, still $2,000.
Source: I literally just went through this process, as a new grad, making slightly above $120k about 3 months ago.