Generally speaking, photography is allowed in most places. At the Tokyo National Museum in Ueno, Japan's equivalent of the British Museum, video and still photography are allowed but not flash. Same with Osaka Castle. I read somewhere that the burst of light from a single flash is roughly equivalent to exposing the object to 1,000 days of sunlight or thereabouts. Use good judgment and avoid using flash if possible. About the only place in Japan that I can recall where all forms of photography were strictly forbidden was Nijo Castle in Kyoto.