Living in the Tokyo area, I have my pick of several teams to visit for games. The Giants and Swallows play downtown; the BayStars are in Yokohama, a little southwest of Tokyo; the Marines are in Chiba, a little east of Tokyo; to the northwest are the Lions. Despite being in the same prefecture (similar to county) as me, Saitama's stadium (the Seibu Dome) is about an hour and a half train ride in nearly a straight line. On game days, an express train runs from Ikebukuro directly to the stadium with just a couple stops, and game attendees from Tokyo should consider that route.
If you want to visit all 12 stadiums, you will need to go to a Lions game. While the stadium is in the Tokyo area, it does take a long time to get there, and unlike every other stadium I know about in Japan, there is almost nothing to do in the area. There's a small amusement park nearby that might be fun for children. Otherwise, this is a long evening of just Seibu trains and baseball.