If you don't like the humidity (and it is BEASTLY in summer), then opt for December through March. On my last trip in early December, it was perfect flipflop and light sweatshirt weather but still warm in the sun. Don't miss products made with beni-imo (purple sweet potato) or unique dishes like sea grapes.
It's debatable. But, I would say during May is the best time. During the winter you can't really swim in the ocean because of Jelly fish. I know people who have gone in May and it was quite nice. However, I would reccomend Okinawa year round! It's a great place! I hear scuba diving is great down there... Also go to the aquariauma. I went to Okinawa World. It was gimmicky a bit, but fun!!
March is not a bad time of the year. It's neither too hot nor too cool and the waters are slightly tingly (makes you feel alive!). Must try are Okinawan champuru (bitter melons sauteed with egg) and everything Spam. There is also a taco restaurant that you MUST visit (I would go back to Okinawa just to have their tacos again). I wrote about it here on Japan Travel. It's called Charlie's Tacos. My friends who went there upon my recommendation agree that it is the BEST place for tacos. http://en.japantravel.com/okinawa/charlies-tacos/27642