As someone from the Midwest I often long for constant spring-like weather, sunny beaches, and a thousand different restaurants to choose from…and then threads like this come up. For $1,500 I could live in a 4 bedroom, 2k SF home with a 10 minute commute.
Sorry that wasn't helpful so I'll try to be here. Using the $3,800 after tax income from earlier, minus the 10% that you'll contribute to a Roth because you're fiscally responsible ($542/mo), minus about $1,500 in rent (hopefully not too much more) brings you to about $1,760 to pay utilities, cable, car payment, eat, party, fill up gas tank, pay for parking/public transit, etc.
For reference, my approximate expenses not including rent/mortgage have averaged $1,200-$1,500 per month. I don't go out of my way to be frugal necessarily, but I also don't consider “shopping” a hobby or anything like that. I also don't have a car payment. So assuming you stayed at that lower end of $1,200 (adjust for the 38% to get to $1,656), you could make it work and still save a decent amount for retirement. Obviously you could save less than 10% and have a little more room. In any event, it will obviously be very very tight, especially if you have a sizable car payment or something. If you are okay with some financial stress early in your career, go for it. The benefits of living there may outweigh the financial stress.