Itinerary for a trip from Tokyo to Fukuoka

The 5th of may I will arrive around 2pm in Narita airport, so I can start travelling the same day or the next morning. Until the 12th or 13th of may I'm planning a trip from Tokyo all the way to Fukuoka with stops in Osaka and Hiroshimaalong the way, I will do this with a JR Pass and I will fly back from Fukuoka to Tokyo. But I have a question about this itinerary: is it doable in this time period with golden week around the same time. I like to see temples and other cultural sights but also like to wonder around in the city. If there is time maybe a day in an onsen would be nice too. As a sidetrip I would definitely like to see Nara when I'm in Osaka, and Miyajima when I'm in Hiroshima. If its possible could someone tell me what would be good to see in the cities/areas mentioned above?
Thanks in advance!

I like to see temples and other cultural sights but also like to wonder around in the city
I'm surprised that Kyoto is not on your list of places, considering it is one of the best places to go for temples and cultural sights.

is it doable in this time period with golden week around the same time
Working under the assumptions that you are leaving Tokyo for 1 week, I would say that your plan is doable. That said, do you have a plan of what to do in Fukuoka? If not, then perhaps you could leave Tokyo first thing on the 6th, travel to Kyoto for 2 nights, Hiroshima/Miyajima for 1 night, Osaka for 2 nights, and Hakone (or somewhere around that region) for 1 night. That would give you one day to get back to Tokyo on the JR pass and saves the additional Fukuoka-Tokyo air ticket. While I do like Fukuoka, I do feel that it does not offer anything extra compared to the other places I listed.

If its possible could someone tell me what would be good to see in the cities/areas mentioned above?
Its all dependent on preference. Check out the Japan-guide listings for each area you are interested in to get a better idea.