There is no pass by that name. Do you mean the JR West Pass for the Kansai area or the Kansai Thru Pass?1. osaka (within the city area including the bay area, ie the tanpozan area, umeda, minami, tenoji, namba?
The Kansai Thru Pass covers Osaka subway, which provides access to almost anywhere in Osaka. The JR pass, on the other hand, is not valid on subways and won't provide you access to, for example, the tempozan area in Osaka Bay.
kyoto, including trip to arashiyama
The Kansai Thru Pass covers everything, but the JR pass is not valid on Kyoto subways and buses, which are the best way to get around Kyoto.
Nara
Both passes cover access to Nara.
Hiroshima city including transportation to Miyajima (if not what is the best way to get to Miyajima)
Neither pass covers access to Hiroshima.
Kobe
Both passes cover access to Kobe. Inside Kobe, the Thru pass is more useful.
It seems the Kansai Thru Pass would cover most, but note that prepaid cards or single tickets could come just as cheap, if not cheaper.