[Firebird]

I cant just answer the question easily, so ill write something about the citys (have been to both) and you can decide.

First off all i dont know about any Ballgames, sorry.

Kobe: The nightview from the mountain is really awesome and a must if you are there. I also really liked Kobe Harbour wich has a huge shopping male, nice restaurants with waterviews (beautifull during sunset), gaming arcades and a small "rollercoaster" park. I personally didnt like the nightarea of Sannomiya. I stayed at a friends house, so i dont know how hard it is to find accomodation in Kobe (many people stay in Osaka or Kyoto)

Hiroshima: The Atomic Bomb Museum here is very good and the park very nice on a sunny day. Not to far away are parts of the innercity with shops and restaurants wich is nice but quite standart (for japanese citys with around 1 millionen). I only heard that the nightlife was good, but i havent experienced it (try wikitravel.org?). I stayed at the Jhoppers wich has a really good location and awesome staff!

If i had to choose i would pick Fukuoka first. Fukuoka is (maybe because close to Korea) a bit different from other Japanese citys. You will find foodvendors along the Canal selling food every evening. Canal city is a huge shoppingcomplex wich was really nice. Nightlife is really good and theres lots of different things to do. I also felt like the city was easier to navigate than Kobe (i know its smaller...).

Otherwise i would go for Hiroshima to see the Museum and because i had a nice time in j hoppers. Than i would drive out to Kobe one evening (from the 3 in Osaka), go to the Harbour area, have dinner and watch the sunset and than take a cable car up the mountain.

Good luck with the hard choice ; )

Edit: Oh yeah, dont plan to much time for Nagasaki, one day is more than enough because theres not much to do in the city. Better take some extra time and drive 1 hour south of Kagoshima to do the hot sand bath wich is a unique experience. Kagoshima itself is also a quite nice city and a good backpackers with the most awesome, cheap dinner is the Little Asia. Beppu is also woth some time to enjoy the hotsprings and see some of the hells ( the red one and the blue one where the best!)