Which Japanese university would be best when studying Japanese abroad?

If learning Japanese is your priority go where you will be immersed as deep as possible. Therefore Tokyo is out, and Akita is a pretty good candidate. I wouldn't worry about the Kansai-ben thing, the average resident of Kansai just does not have a overpowering accent. Living there is not going to give you an impenetrable accent any more than living in NYC would make one talk like Bobby DeNiro in "Mean Streets".