Hiroyuki gave you some good advice. Go see Shuri castle, then also put the Churaumi aquarium on your list and while you are up that way visit the pinapple farms and taste some pinapple wine. Take the ferry over to Ie Shima for a nice little day trip. It will be very hot and humid when you visit, so dress accordingly.
As he said, the rain should be over by then, but typhoon season is still on. Enjoy your trip.