Explore the island. It has a lot of scenic beauty, so you should take your time and literally stop to smell the roses (and all the other tropical flowers along the way).
If you're looking for something that the locals do, ask around and find Hamura's Saimin. Saimin is a local food item, primarily composed of noodles in broth. You can have it with cabbage, fishcake, won ton (steamed pork in wheat wrappers), and beef or chicken sticks (pieces of grilled beef or chicken skewered on short bamboo sticks). Saimin is great on cold days, hot days, after a long day, early in the morning after going out or spending time at a friend's house. Hamura's is one of the few places that's open at 2 a.m., so lots of people go there after drinking or partying.
Don't expect great ambiance. It's a small building off a side street in Lihue town. When you get there, park, and walk to the building. There are screen doors that open, and when you walk in, everyone looks up to see who just came in. Lihue is a small town. Sometimes it's busy and you just stand there and wait for the next available stool to open up. Yes, there are simply stools at formica lunch counters. You can chat with your 'neighbors' or just watch the kitchen people make everyone's saimin. The saimin comes in several sizes, so just order by size, and by what you want in it. It's a family run business, so be nice. It's a great place to go if you like noodles in broth.
Fondest memory: Having someone say, 'Let's go to Hamura's!' at midnight. Everyone piles into the car and we drive to Hamura's Saimin and have our late night snack before going to bed.
Kauai is the Garden Isle, the scenery is breathtaking. From the mountians to the sea it is one beautiful view after another. An absolute must is just to look around you.
Fondest memory: Kauai is the first place that I ever set foot on American soil. Who could ask for a better place for their first visit. It is truly paradise.