1. Say yes to everything.
Session at a bass players house? Yes. Gig in Jersey City for $40, toll money, and dinner? Yes. Singer's demo recording session? Yes. High school musical in White Plains? Yes. Jam session at the Tea Lounge? Yes. Say yes for moral and financial reasons. Take it all, play your ass off, and be cool.
2. Go hear everyone play, especially older jazz musicians.
Pay the cover, buy the drink, sit in the front. Don't worry if the music is good, bad, or indifferent. You will learn something. Any conclusion you draw is likely to change in a few months anyway.
3. Assume every musician you meet, on any gig, in any scene, of any age, of any background, is very, very good.
This is not an arts-friendly cheap-living European capitol This is not a Midwest college town. This is New York. Most musicians moved here from somewhere far away to achieve their life's dream. If they have lived here longer than you, they know something you don't, and are very, very good at something. So be cool.
4.) Give every musician you meet a reason to notice you.
I do not know how many musicians move to New York ever year. I do know that very, very few of them stay. Therefore, if you tell an older musician, "I just moved to town", that older musician is quite reasonably seeing you as one of many. If you wish to stand out, play as well as you can, and be friendly, polite, and sincere. You might be surprised how many people notice.
5.) Be generous in praising and supporting friends, colleagues, and peers.
Your friend, who moved here with you, gets a great gig, while you are hoping to maybe sit in somewhere. Go to his or her gig, and cheer him or her on. At a jam session, you are outplayed by someone your age. Try to make some connection with that person. Again, this will be better morally and materially, and no, this is not easy.
6.) Have extremely clear goals, and go right to work achieving them.
A very clear goal might be very general: "Check out NYC jazz and/or the music scene in general!" Maybe you're more specific: "I want this band, with these people, to play these tunes, at this place, for this amount of people, x number of times per year/month/week". Excellent. Get cracking. Not sure of your goal? No problem. Just acknowledge that you're unsure. You'll figure it out.