I like Shuri Castle in Okinawa, although that is the real palace of the Ryūkyū Kingdom, which is a reconstructed copy. According to Wikipedia, the original one is almost destroyed during the second world war. It looks beautiful and can show the royal family life. Moreover, there is an exhibition to show the history of Okinawa and the king life. That is very very informative. Besides, the scenic from there looks beautiful too.
I love there. That is a must visit spot in Okinawa.