Welcome to Big Game Hunt.
I'm from Nova Scotia Canada so I'd be the last person to give you advice on hunting in New York City, but would suspect that you can't.
My best advice is "get proper legal advice" not the neighbour, " the guy that used to be a cop" the lady that "works for a lawyer" etc.
Doing something wrong"illegal" can really screw you up, now and for years to come.
Giving all that, lots of Topics, join in

You misunderstood. I live in NYC but I want to go hunting in New York State. I know you can't hunt anything in the city. I wanted to know if anything knows anything about keeping hunting rifles/weapons at home in NYC or if there are any laws that prohibit it. I know that you're allowed to keep hunting weapons at home if you live in New York State.

Ok, you can probably go to a Firearms Dealer,Shooting Club,Goverment website etc and get the info you want;
i.e.
There is no state license requirement for the possession of a rifle or shotgun, so long as the rifle has barrel(s) at least 16 inches in length and the shotgun has barrel(s) at least 18 inches in length.

It is unlawful for any person convicted of a felony, other serious offense, or who been certified as not suitable to possess a rifle or shotgun (mentally incompetent) to possess a firearm.

Generally, it is unlawful for anyone under the age of 16 to possess any firearm; however, a rifle or shotgun may be possessed by a person between 12 and 16 who is engaged in target shooting on a range supervised by a military officer, certified instructor, or a parent, guardian or a person over the age of eighteen designated in writing by such parent or guardian provided the adult has a hunter safety certificate.

It is unlawful to possess 20 or more firearms as defined under NY law outside one's home or business.

You gotta due some research, hunter safety, safe storage etc. The above was just a little tidbit, not to be confused with the proper interpetation of The Laws & Regulations.

From the NRA website........click this link.
Good Luck!

http://www.nraila.org/GunLaws/nyc.aspx

That's what I'm doing now. I know about the 10 hour certification class. I've read through the online course which goes over firearm safety as well.

Thanks. That makes sense. Here's another question: Where to you apply for all this? It says the police commissioner issues the license (if the requirements are met) but doesn't say where to submit all the paperwork. Do I submit it at the police station or where?

Yeah, I'm pretty sure you would have to go to the police station to do this. In New Jersey we need to go the state police, fill out the paper work and then wait until they do thier investigation before we can get the firearm buyers permit. I would imagine it is similar in NYC. They will be able to point you in the right direction. If you run into someone that is not being very helpful......try a different station! Ask for some pointers as to how to answer the questions because there may be some red flag words they look for and you don't want to put those down. In NJ when they ask why you want a firearm you want to say for "target practice" I don't know why but I was told that if you put that down, they won't question it.
Good luck and don't ley ANYONE try to talk you out of excersising your constitutional rights!

Got it. That was very helpful. Thanks a lot.