Kauai has the "wettest spot on earth" (Mt. Waialeale) and Waimea Canyon is not a big canyon for nothing! It is especially wet during the winter months.

The Kona side of the Big Island averages 9 inches of rain a year. So this would certainly be one of my islands of choice in the winter. You can see the volcano and Hilo (on the "wet" side) on day trips. You can ski in the morning (Mauna Kea) and surf in the afternoon. Lots to see and do. It's true that there are not many white sand beaches in most parts of the island, but there is water and beaches everywhere.

My second choice would be Maui. There are lovely beaches, Haleakala, ziplining in Kapalua (http://tinyurl.com/39gdv7), snorkling, and great dining.