JR West - Sanyo

Is it possible to visit Kyoto, Nara and Kobe in 1 day? This is my 1st trip to Japan and I'm not sure how many days to stay in Osaka city. Is it the local train to go to these cities or do I buy the bullet train JR pass?

I intend to travel to Hiroshima city on another day and visit the Atomic Bomb Dome in the morning, then proceed to Hakata later that day.

How much is the daily JR West Sanyo ticket from Osaka to Hiroshima to Hakata?

I will stay a night at Hakata and fly to Seoul in the afternoon.

Any suggestions?

Is it possible to visit Kyoto, Nara and Kobe in 1 day?

All of these cities are connected with each other in under an hour by local trains. So, it is definitely possible to visit them all in a single day. Of course, you will have only very limited time in each city for sightseeing.

Please use the transportation pages of this website and/or Hyperdia to look up access information.

For Kyoto:
http://www.japan-guide.com/e/e2363.html

For Nara:
http://www.japan-guide.com/e/e4107.html

For Kobe:
http://www.japan-guide.com/e/e3554.html

For Osaka:
http://www.japan-guide.com/e/e4006.html

How much is the daily JR West Sanyo ticket from Osaka to Hiroshima to Hakata?

I don't know what you mean with "daily JR West Sanyo ticket", but the regular fare from Hiroshima to Hakata by shinkansen is around 8500-9000 yen one way, as can be looked up by Hyperdia:
http://www.hyperdia.com/

In case you refer to the Sanyo Area Pass, note that it has just been discontinued:
http://www.japan-guide.com/e/e2361_04.html

An alternative pass is the following one, but I don't think it pays off for a one way trip from Osaka to Hakata and some urban transportation around Osaka:
http://www.japan-guide.com/e/e2361_sanyo_sanin.html

note that it has just been discontinued

I correct myself. It is still available for another two weeks, but not a good value.