Yokohama is a really nice place. I like it better than Tokyo in many ways. You could make a day trip there and include a ball game.

From watching games on TV, the Nagoya Dome (or whatever it is called) looks like the most sterile and dull ballpark in Japan. Always lots and lots of empty seats.

Oh, you can completely self cater in Japan for sporting events. I once saw a guy bring an entire thermos-barrel of soup. They have ok food at the ballpark, but I usually picked up some decent quality sushi from a department store and brought some Yona-Yona beer (microbrew). Technically, you can't bring cans and glass bottles, but they never check your bags. For football (soccer) they actually search your bags and it became a great sport to smuggle them in. They have tables where you are supposed to pour your beer into paper cups. They are convinced that hooliganism is linked to football even though the fans are as straightlaced as you can imagine.