I've been to Kauai a few times. My wife and I love the place.
TAKE MY ADVICE AND GET THIS BOOK:
http://search.barnesandnoble.com/Ultimate-Kauai-Guidebook/Andrew-Doughty/e/9780981461014/?itm=1
I didn't write it or anything.
It has great advice for beaches and restaurants and places to visit. The beach reviews are great. We spent days visiting all the secluded beaches he recommended. It was great. His restaurant recommendations were all spot on.
Other things to do:
Goto Duane's Ono Char Burger. That place is freaking awesome. It's on the main road on the east/northeast side of the island.
Goto Puka Dog on the south side of the island. Really yummy and different hotdogs.
Take a helicopter ride. In a helicopter you can get a view of the Napali Coast, which is totally incredible and inaccesible by car. You can also get into the crater in the center of the island which is an amazing site to see. It's the wettest spot on Earth. You get into it and you're almost totally surrounded by waterfalls.
With a 2 year old with us, our last trip there was limited to more domestic activities, so we spent a lot of time trying to find the best shave ice on the island. Shave ice is awesome. We didn't find one that topped the shave ice on Maui, though.