New Jersey... requires you keep the gun in your trunk, unloaded, in a locked container. Ammo must be contained in another container. No hollow-points. Whatever you do... don't carry the gun. NJ allows non-residents to come for training, shooting sports, to gun ranges, etc. You can't carry though. Just follow the law there and make sure you have your home-state CCW permit with you.
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New York... Keep the gun in the trunk as you enter from NJ. Drive straight through without stopping. It's less than an hour of total time you'll be in NYS. Stay completely away from NYC any of it's burrows or New York County. Come North on the NYS Thruway and then East on Rt. 84 at the Newburgh exit. You'll enter Connecticut at Danbury within about an hour. If you're coming from PA just take Rt. 84 from PA into CT... it's about a 75 minute drive. You'll be way North of the city and won't get hassled by the upstate police.
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Make sure you stay to the speed limit, use your signals, make sure your inspection and reg are current. NYS does not require you notify LE when stopped (unless asked).