Look up beastskills.com, tricktutorials.com and just drilssandskills.com
They provide good explanations and progressions.
Also, at least in europe, parkour groups are very open and very nice people. Maybe try to contact them first(most have a facebook page,forums or other means to coordinate meetups) and ask if they offer an open training for newbies, or if a couple of them can show you the ropes. Since you are in NYC ( which as every european who has never been there knows is a cesspool of crime and violence;) maybe show up with a couple of friends or your parents nearby, but it shouldn't be a problem.
If that doesn't work out, watch tutorials on youtube and imitate. Start with landings, precision jumps and rolls. These are INCREDIBLY important to protect your joints, back, everything. Then move to vaults, wall runs etc.
Below are some pointers that I wish I had known when I started, but you NEED to watch tutorials, and lots of them. Everyone does the movements a bit differently, so you might have to search around a bit.
First do landings:
start out jumping UP from low stuff(<30cm), work your way up
SLOWLY and always aim for perfect form. This is landing on the balls of your feet, never letting the heels touch the ground, and trying to keep the angle between the legs >=90 degrees. You can let yourself dip forward and stop the rest of the impact with your arms or continue into a roll. You can easily tell if you did a bad landing by listening, a good landing is hardly audible at all.
Second, precision jumps:
Start nearly at ground level, maybe by jumping between logs, bricks ( very nice for impact control as they will move if done badly) or just jumping on the edge of the sidewalk. You want to always come in from above, so you always need to jump UP a bit, even for a long jump. What you want is a parabolic arc, that way you can use the landing technique you just learned. Try to land exactly at the edge, so that only the balls of the feet, make contact. Keep your eyes on the place you want to land at all times! A perfect precision jump consists of a perfect landing ( barely audible) and perfect momentum control (coming in from above and not in a straight forward line so you don't move or fall forward).
Lastly the rolls:
watch tutorials(!), then try it on concrete. You need to get a feel for the impact, and grass or soft gym floor doesn't give you that ( You CAN use grass or the slightly springy ground you can find in sprinter lanes if you need to overcome fear and get the basic movement down, but should switch as soon as possible).
Start out rolling from a squatting position, then follow by jumping forward and up a little bit and try to do a fluid movement - not landing =>stop=>jump into roll but landing=>during the lowering into the 90 ° position decide if you need to roll ( this will become instinct pretty soon)=>converting the remainder of momentum into a rolling motion.
*TL;DR: Look up the websites in the first sentence, try the groups, watch tutorials and imitate, do it SLOWLY, CAREFULLY and always be in control *
Hope this helps, have fun