I used to drive a lot for work to New York City. I live in Ohio so the drive wasn't as bad, only about 6 hours. However, I learned a lot about road warriors.
First, make sure your car is in proper shape to make the trip. Check your fluids and if you were due for any service, make sure it is complete before you make the trip.
Second, don't be scared to just pull over and sleep if you get tired. It is absolutely not worth rushing a long drive. If you fall asleep behind the wheel, you're in trouble.
Third, bring enough music to keep you entertained. You are going to get bored. It happens. Music helped me get through the really boring parts.
Fourth, respect semi drivers. Those guys drive professionally. They know what they are doing (usually). Be a courteous driver in general, but if a truck driver needs to change lanes, I always let them.
Fifth, make sure you know your route before leaving. Do not get lost out there. It sucks.
Sixth, look for places to park before you get the NYC. Owning a car is essentially a sin in that city. You will pay out the ass for parking and you need to find a good spot that is safe and cheap before you get there. Stick to the main brand lots like Central or ICON.
Last, if you don't have an EZ-Pass, you need to get one. I drove ONCE to NYC without an EZ-Pass and I will NEVER make that mistake again. Trust me, you don't want to have to deal with cash when there are 25 cars behind you that are PISSED because you took more than 2 seconds to get through the toll booth.
Depending on how you enter NYC, it can cost a lot in tolls. Have enough money for them or you will be fucked when your stuck at a booth with no money (or EZ-Pass). The Lincoln Tunnel was $13 when entering the city. I used to stay in NJ so it cost my company $13 bucks every freaking day for me to drive in there.
Also, enjoy the city. I spent a lot of time there and most of it was at work. But when I got to go out and explore, it really is one of the greatest cities out there. So much to do.
Oh, and avoid New Jersey as much as possible. The drivers in NJ near the NY border are a different type of animal and you're best to just avoid that area.
Enjoy your trip.