After you've gained some experience fishing from a kayak you're ready to head out at night. It's my favorite time to fish in the summer as many of our gamefish are more active and the waters are less crowded. Many places can't even be accessed during the day. The northern NJ shore is such a place. There's simply too much activity going on and there are many limitations on where you can launch.
Besides many game fish are more easily caught at night. They often move into areas where they're much easier targets for you and your kayak too. Stripers and weakfish move shallow and bluefish become scarcer. In freshwater all the basses (smallies, largemouths and hybrids), walleyes, catfish, etc. are easier to catch too. Some lakes experience a phenomenon where from approximately midnight to 5 AM the herring feed on the surface in large schools and the predator's concentrate on the bounty. It can be spectacular fishing for fish that rival saltwater sizes. Double digit hybrids and walleyes on light tackle will give you all the sport you could every want and you'll have it all to yourself too.
It takes a bit of adjustment when converting to night kayak fishing. As one looses the ability to see well the other senses will compensate; especially your hearing and to a lesser degree your sense of smell will contribute more. Often fish will move into areas that are too shallow for them to feel comfortable during the day. Please become comfortable with your kayak with a lot of daytime kayak fishing first before taking on the dark especially if those forays are going to be in the salt. You may wish to go freshwater fishing for your initial forays as the smaller water and lack of tides and currents will give you less to deal with and adjust to. Nighttime is not the time to learn the sport. Once you've become comfortable with your kayak and gear adding some night excursions may be just what you need to spice up your kayak fishing. In the summer we do a lot more night fishing then in the daytime. Even if you don't plan on fishing in the dark the best fishing often occurs during predawn and sunset. To be out on the water and ready to fish at these times you'll need to paddle in one direction in the dark. So you'll need to have some night fishing gear anyway.
I highly recommended that you don't go night kayak fishing alone. I often fish in daylight alone but rarely at night and never in the salt. Keep it simple at night too, especially in the beginning. Try to use single hook barbless lures and if you're fly fishing wear clear glasses to protect your eyes. Have specific places where you keep things and always place them there. It's also a good idea to fish areas that you've fished in the daylight so you'll be familiar with them. 
There is additional equipment that's going to be required beyond what you generally carry to fish during the day. Since its dark you're going to need lights. Not only to be seen but to see as well. You're required to carry a bright flashlight at night in NJ waters. Some guys like to hard wire running lights just like a boat. I don't agree with this set up, as there is the potential for a problem. Should you be out in open water an approaching boat might think that you're a boat. If they have the right of way they may not recognize that you aren't a boat and don't have the ability to adjust to them. I'm an advocate of a bright 360-degree white light that is raised above your head. It can be on a pole so it has an unobstructed view. The boat would interpret a light like this as a stationary object and they would proceed with caution. The one that I'm using is a LED and can be seen for miles. I put it in a 3-foot piece of PVC and simply taped it in place. Eventually I'll do more but it works. I then place it in a rod holder that doesn't have a rod in it and I'm set. I only have it one when I want to be seen. The rest of the time it's turned off so I don't ruin my night vision. Most of the places I fish are spots where boats don't even go during the day, let alone at night. As always you need to exercise common sense and err on the side of caution. I also carry a few other lights. One is a waterproof headlamp. The one I use is a LED and has 3 brightness settings and a flasher mode. This is on my cap the entire time that I'm out on the water at night. I also have a small red light on my cap. The red light doesn't affect my night vision and provides sufficient light to rig and most things I need to do. It also doesn't spook the fish either as they can't see it. On my pfd I have a pfd light. It's a 360-degree waterproof light that I will use should I fall in and loose the kayak. Lastly I have a small waterproof flashlight around my neck as a backup.
It's easy to get disoriented while on the water in the dark. So I feel that either a compass or GPS is important. You'll be amazed at how easily you can mistake where you initiated your fishing. A GPS has already saved me considerable paddling to places where I thought I had launched from.
You and your night kayak fishing buddies can easily loose track of one another. Yelling not only can disturb the fish but also has a very limited range. We like to bring both 2-way FRS radios and our cell phones. Having ruined a few radios and not wishing to ruin my cell phone I keep both in a waterproof, floating case that is attached to the kayak. These cases allow you to talk while they are fully protected. They come in very handy and all cell plans have free nights too.
In some areas bug spray can be invaluable so it's a good idea to bring it along. Some terrific fishing is available in the estuaries at night and if there isn't a breeze the local inhabitants can be very annoying. Sometimes you just can't fish an area, as the bugs will eat you alive.
The best places to fish at night sometimes differ from the best daylight spots. Sometimes they're the same. Most game fish will move into the shallows to feed under the cover of darkness. It's very important that you keep noise to a minimum or you could alert them that you're there. A quiet kayak is very important. Have everything rigged before you hit the area you intend to fish and be as stealthy as you can. If you're doing it right you'll end up spooking some fish as your kayak gets right next to them. The explosion of a big fish right next to you is amazing. Just make sure when you jump that you land in the kayak and not the water. Be prepared for a hit at any time, as often you'll get a hit as you're lifting the lure out of the water. Hang on and let the fish take the line.
There are some specific lures and techniques that we find work well at night. For Stripers the Tube in Worm is king. Often we don't use any other method. Other offerings are black swimmers like mambo minnows, megabaits, bombers, tsunamis, etc. Single hook jig plastics like tsunamis and wildeyes are good to have in the arsenal. Sluggos are great that they're a single hook lure. I like both the 9 and 6 inch when there aren't bluefish around. When fishing flies I prefer black ones that move some water. I highly recommend keeping it simple as to lure choices. I'm guilty of always carrying too much stuff but I can narrow it down to just a few offerings.