Osaka, Kyoto , Kobe and Nara are just 20-30 minutes away from each other.
I think it would be best if you stay in Osaka, since it is convenient to reach Kobe,Kyoto and Nara from there.
Night Life in Kobe? ... yup yup yup.. although I'm not quite familiar where since I'm not that interested in that, but most of my friends here would spend a night in Kobe, drinking, dancing, playing billiards till wee hours in the morning... it is a lively city.
I can probably show you some shopping area here in Osaka, and Kobe on the weekend... just contact me here
anyway enjoy..