I second going to see the Swallows.
You have to love a stadium with history like this:
The second oldest professional ballpark still in use, Jingu's brick walls date back to 1926. Before the Second World War, Babe Ruth and Lou Gehrig played in Jingu during an exhibition tour of Japan. Though renovated in 1982, no other stadium in Eastern Japan retains as much history and old-ballpark style.