As a soccer culture guy, it was an amazing experience to go to a baseball match for the first time. Maybe the Tokyo Dome won't make an impression in an American, but I think it's really spectacular. It's the Yomiouri Giants home stadium and includes the Japanese Baseball Hall of Fame, restaurants, shops, a hotel and even an amusement park called LaQua. As the soccer stadiums in Europe, it helds the biggest concerts in the city as well.
It's a fun but bit dated amusement park with an outdoor shopping and restaurant area. The dome itself is quite good for concerts though, I saw X-Japan there 2008 and it was a nice experience.