We stayed on the east side, was cheap and let us get anywhere quickly, but definitely not as scenic. I said if I went back I'd stay in the Princeville area, but rain MAY be an issue.
Napali coast is an absolute must. I agree with others that the open door helicopter ride was a thrill, but you should know a few things about it. It's very loud. You won't be having any conversations while you are on the trip. Also, by the end, my eyes were watering because of the wind, despite wearing eye covering. And finally... we opted to see the Napali coast that way, and it was absolutely breathtaking, but man, it was over before it began. If I had it to do again, and it was one or the other, I'd do that by boat. In November, that choice may be made for you, as some boats don't go out on that coast side due to high surf typical that time of year. That was true when I was there in January, November might be ok.
The "Grand Canyon" of Hawaii is a must see. It is also where the hiking over the top of the Napali coast is that was mentioned above.
The south side beaches will give you the clearest and calmest water, but a little less scenic. There is a great blowhole there that has easy parking.
The Princeville Resort (used to be the St. Regis) is a spectacular place to watch a sunset. You can have dinner there without staying there, but it's currently under construction, not sure when it is reopening.
Kauai is full of things to see and do, the guidebook mentioned above (Kauai Revealed) will help you find everyone, whether you want to see waterfalls, hike, find a perfect beach, float a river, boat, helicopter, or surf.