Osaka Dome (Kiyocera Dome/Kyocera Dome): An ORIX Buffaloes Game
Technically, the Buffaloes have been around quite some time too, with the predecessor founded in 1936. But originally, that team was the Hankyu Braves, the ORIX Braves, the ORIX BlueWave, and finally merged with Kintetsu (whose team was formed in 1950) in 2005 to form the ORIX Buffaloes.
The Braves/BlueWave/Buffaloes have always called Kansai their home, and enjoyed success in the late 1960s through the 1970s and again in the mid-1990s when Ichiro was a member. But moving from Nishinomiya to Kobe, and then Osaka after the merger, has probably had some effect, and the lack of a strong rival and an identity crisis hasn't helped things.
I should mention that the Buffaloes play a few games each month in Kobe, the prior home of the ORIX BlueWave. Seeing a game there requires good timing and planning, and games seem to only be on weekdays or an occasional Saturday.
I arrived before the gates opened, a rarity in the past couple of years as I've often been sightseeing in the afternoon. There were two fairly long lines to get in, one for each of the cheering groups. They get there early to secure their seats in the general admission outfield.
It's located on the southeast end of the JR Osaka Loop Line. You can get off at Taisho Station and walk about five minutes west, heading toward the crazy metal wave behind the water storage balls.
Alternately, the Hanshin Namba Line and Nagahori Tsurumi-ryokuchi subway line stop one block from the stadium, but unless you're already on those lines it's usually quite an inconvenient station. The Tsurumi-ryokuchi line goes to Osaka Castle, so that might be a good way to get there. The block between the station and the stadium is an entertainment district with several restaurants and the team souvenir shop.