I feel that Yokohama is somewhat overlooked. Although a 30 minute train ride from Shibuya will get you there, somehow it has been submerged, taken for granted as a part of the sprawl that is Tokyo.
Admittedly, to some extent I am also guilty of this. A lot of my time is spent around Tokyo, with occasional side trips. To remedy this on a fine day we went off to explore the Motomachi/Yamate area, with its air of Meiji nostalgia and opportunities for walkies.
The old houses of diplomats and other of Japan's first non-Japanese residents sit upon a hill, brilliant in paint and copper, interspersed with fancy tea houses and the Foreign Cemetary, a testament to Japan's evolution towards being a more cosmopolitan nation. I was pleasantly surprised to see that many non-Japanese women were buried with their Japanese husbands, which gives me yet more ammo for when people say that the 'gyaku-kokusai couple' is a recent phenomenon.