You don't say where in NJ you are starting from. Assuming it will be Newark, I would just do the simplest thing and take I-80 west into Pennsylvania, then take I-380 west/north to Scranton, then get onto I-81 north and take it to Syracuse, then I-90 west to Buffalo.
Snow is a considerable risk on the PA and NY parts of your route. You will do yourself a favor by staying on the major highways, as they are the most likely to get cleared quickly. This route is boring as all get out, but it will be the safest. Drive carefully. If you do not have experience driving in snow, get off the road and wait for the roads to clear up before continuing.