If you want to stay on a nice swimmable beach Sheraton (Poipu) will probably the best choice. I believe it is also walking distance to a bunch of restaurants. And in November, there should be less chance of rain in the south.
But my favorite activities are on the North Shore:
-Hike Napali coast (this can be 3-6 hours depending on how far you want to go).
-snorkel at Tunnels and Kee. But come to think of it, can one even snorkel at any of the beaches in the north in November?

South and West:
-Waimea Canyon
-snorkel Poipu beach

I'm not as familiar with the eastern part of the island. The first time we went to Kauai we did stay by the airport but I remember just driving out to see the sights and going back to the hotel just to sleep.