There are three main things on the to-do list for a visit to Kauai. First is a hike along the edge of the Na-Pali coast, simply follow the road till the end and look for the signs. I suggest a good pair of shoes/boots and a water bottle or two. Definitely remember the camera with extra batteries and lots of film (you will be disappointed otherwise, trust me).
Secondly is the drive up into the canyon, we did it three times although I would recommend waiting for a clear day as it makes the final lookout all the better.
Third is the beach on the west coast at the state park. Definitely off the beaten path but sensational.
Quick Tips:
Do the outdoorsy things and save the Luau's etc for later!
Best Way To Get Around:
You must rent a car to see all of the things the island has to offer. The day that you rent it on has a lot to do with pricing so if it seems high then only rent it for a day or two and come back. We got a jeep for only slightly more than we had originally paid for a Neon!