Sannomiya ward is where downtown Kobe city and all the visitor attractions are located. So, if you need to go to downtown Kobe, you need to get to Sannomiya.
Sannomiya ward is serviced by both Japan Railway (JR) and Hankyu Railway. This line of Hankyu Railway runs from Kyoto City, so if you are staying in Kyoto, you can get to downtown Kobe either by Hankyu railway or Japan Railway.
This video shows the Hankyu Railway Sannomiya Station （阪急三宮駅）. Enjoy!!
AloJapan.com