Hi, I've played jazz flute for years and have been in several bands, including leading my own jazz fusion band. So I've known many, many musicians, including some who came to NYC with no money, no job, just wanting to be here for the music. You're not alone in your dream, and that's a helpful thing.
Here are some scenarios I know of: A drummer from Italy who rented a sofa to sleep on in a hallway, with access to a bathroom, for $275/month; a violinist who roomed with three other musicians, but she had her own alcove that she sectioned off with a curtain; a songwriter who lives in a basement in the suburbs for $650/month; a playwright who pays about $450/month for a room in Brooklyn that is so small, only his bed a few other things will fit. Sitting on the bed, his knees hit the door. There are internet sources for these room rentals (craig's list et al) but contacts are always the best way to go.
All of them would tell you it's tough. Some have used food pantries for a meal now and then. Some are living without health insurance. Some break the law once in awhile to get by.
The most common day job people have is in food service. You can work breakfast and lunch shifts, or only lunch, or only 4 days a week all day, and then hit the clubs and jam sessions at night and weekends. (I assume you play some instrument?). Janitor jobs you are unlikely to get, a lot of those are union jobs. Temp jobs are highly competitive right now; I know a guy with an ivy league B.S. degree who can't get one. Also, note most jam sessions happen Monday-Wednesday nights, but there are exceptions. Any job you have must fit around the music.
If I were you I would get food service job experience where you are, and save up all the money possible. It would help immensely if your parents are supportive in case your plans fall through, or you get into trouble financially and need a gift or a loan. Also, don't forget that Rochester has a great music scene and if you can hang out there, you might meet some people who are heading south some time soon.
It would also help to be a few years older. The best room mate situations involve people who are older than you, in their 20's, and many would not accept such a young person for fear you'd be irresponsible. It's not fair, I know, but I know it happens. Any contacts you can find around NYC who are in their 20's could be a great help as well. Above all--no illegal drugs in your life. They don't improve the music but they do screw up your life in multiple ways. Also, practice now cutting expenses and learning how to live with less. And I do hope all your dream comes true.
Licensed Real Estate Salesperson
New York, NY