NYC is highly expensive and I'm assuming you meaning Manhattan.
I'm ganna try to break it down:
For World Class BJJ- Renzo Academy is the place. They have bout a dozen or so BlackBelt instructor there that can get you gear up for any Gi/NoGi competition. However i do believe for their Blue belt program (2-3 years) its somewhere between $240/month and up. As you progress (in strips and then promotion in purple, brown, black) its only going to get more expensive.
Other BJJ place is cheaper- My old gym Fighthouse is only $120 a month and if you want to learn Muay Thai in addition to BJJ its $190/mon
remember though if you want to learn more and not limited to BJJ only:
Ronin Athletics is a great place. For $200 (i believe) you get MMA training including: wrestling, BJJ, and striking. I highly recommend these place but there are more: Combat Fighting Systems, Combined Martial Arts Academy, and a Sambo gym there as well.
Vitor Shaolin Ribeiro got a successful gym 200 down intially, and than just 150 a month after that.
he has several instructors there, classes from early like 7 am, until about 9 at night, so they are there all day.
if your a new yorker, its worth it.
renzo gracie gym...hes never there, bc hes always doing business else where.
and vitor is always there, making sure things are running smoothly.