Kauai is my favorite topic (and place!)on Earth. My mom has five timeshares there so we usually go five times a year and I am happy to help in any way I can.
Waimea Canyon is a good start. I would say that and the Na Pali coast are the two must-see scenic spots. Na Pali is really only accessible by boat or helicopter - I have done both and recommend both. I think it is the most beautiful spot on Earth.
I don't know if you are staying on the South Shore, North Shore or Coconut Coast, but if you have time you should try to spend a day in all three. In the South Shore, there are nice beach spots in Poipu, and some fun shopping in both Poipu and Koloa. You should also drop by Spouting Horn in Poipu if you get a chance.
On the North Shore, Princeville and Hanalei are both very popular spots. And in Kapa'a, you will find a lot of great shops and restaurants, as well as a Kauai Products Fair on Kuhio highway.
For food, I would say if you want a place with a great view, Beach House in Poipu is gorgeous. Gaylord's in Lihue has a very nice plantation feel ambience and is a good spot for lunch or dinner.
If you like Korean, the Korean BBQ in Kapa'a at Kinipopo is the best I have ever had. There is pretty good Mexican (for Hawaii standards) in the same shopping center at Monico's. Great burgers are at Duane's Ono Charburger in Anahola, Brick Oven Pizza is great in Kapa'a and Kalaheo, Pukadogs hot dogs in Poipu are good, and the chili is tasty at Bubba's. There are also good plate lunches at Mark's Place in Lihue.
If you like rum, don't miss Koloa Rum Company's free tastings every half hour - they are at Kilohana Plantation in Lihue (in the same lot as Gaylord's).
For shopping, Kukui'ula in Poipu has higher end art, jewelry, and clothes. Kukui Grove is the main shopping mall in Lihue. But get your mac nuts and coffee souvenirs at Costco or Walmart in Lihue - gas for your rental car is also MUCH cheaper at Costco.
If you have any other questions, I am happy to help if I can...