Exploring Kyoto, Osaka, and Hiroshima

We plan to spend 5 nights in Tokyo and 6 nights exploring Kyoto, Osaka, Hiroshima and 3 nights in Fukuoka where we fly out of.

Would it be best to stay in Kyoto and do day trips or stay in each place? We have a 7 day JR Pass.

It comes down to personal preference: spending the night in each city versus luggage complication.

As Uji suggested, it depends what you prefer.

If it was me I would spend two nights in Kyoto. Visit Osaka on a day trip from Kyoto (roughly 25 mins each way by train).

I would spend one night in Hiroshima. Kyoto to Hiroshima is roughly two hours so it doesn't really make sense to backtrack the two hours to Kyoto to stay overnight in Kyoto and then spend two hours the following day to travel back past Hiroshima and then another 1.25 hours on to Fukuoka.

Depending on your budget and what you plan to do in Hiroshima I would consider spending a night on Miyajima instead of in Hiroshima City itself:-
http://www.japan-guide.com/e/e3401.html

And again depending on budget you may wish to consider a stay in a Ryokan (Traditional Inn) in Kyoto.
http://www.japan-guide.com/e/e2029.html

Enjoy your trip!

I misread your original question, so I would spend five nights in Kyoto, and one night in Hiroshima/Miyajima.

Well it looks like you too have to go through the classic dilemma - there is nothing worse on a vacation than dragging luggage around like
and albatross around your neck, but to avoid that will rob you of your most precious asset which is time.
So it is up to you - if you are elderly or something than switching lodging as little as possible might make sense, but otherwise if I were you I'd emphasize that time is more important and GC3 gives some good advice.
Five nights in Tokyo is more than enough to see many of the good sights, so if you haven't been there yet seeing Kamakura as a day trip is well worth it, as well as Hakone and the Fuji 5 lakes for a day. In Kansai also be sure to spend a day in Nara.
This site has some good info on what to see in all the cities, plus you might want to look at:
http://www.jnto.go.jp
http://www.ar.jal.com/world/en/guidetojapan/city_information/tyo/see/a...
http://www.pref.kyoto.jp/visitkyoto/en/
http://www.ar.jal.com/world/en/guidetojapan/city_information/uky/see/c...
http://www.tinyurl.com/see-fukuoka

I agree with Uji, it's personal preference. I had a similar trip and bases ourselves in Osaka for 10 days and did day trips to Kyoto (we recommend staying at least overnight), Mt Koya, Takahashi and an overnight stay in Hiroshima.

I'm not very interested in temples and shrines and preferred to stay in the city so that's why we were based in Osaka. The accommodation in Osaka was fairly inexpensive (Hearton Hotel Shinsaibashi) so we could afford to leave luggage in our room while we went to Hiroshima.

In Hiroshima we stayed in a Toyoko Inn close to the train station which was also near the tram line so was a very convenient location. I preferred that over staying in Miyajima, but you might like to experience a ryokan.

Hope that helps, maybe give you some things to think about.

Thanks for the insight into exploring these and other places, and information on accomodation, this will be very helpful.

I have another question, can you catch a train (using our JR pass) direct from Hiroshima to Fukuoka as a timetable I sighted stated you need to return to Kyoto or Osaka then to Fukuoka.

can you catch a train (using our JR pass) direct from Hiroshima to Fukuoka

Yes, I think all of the Shinkansen go direct between these two cities.

as a timetable I sighted stated you need to return to Kyoto or Osaka then to Fukuoka.

That is probably because you used the station with the name "Fukuoka", which is a station in Toyama prefecture on the Hokuriku main line (ie north of Kyoto/Osaka, past Kanazawa)
http://en.wikipedia.org/wiki/Fukuoka_Station
http://en.wikipedia.org/wiki/Hokuriku_Main_Line

When searching timetables for Fukuoka (the city) use the station name "Hakata" which is the Shinkansen station in Fukuoka (the city).

Thank you!

I wonder how common that mistake is. Back when I first went to Japan I had looked up prices to go to Fukuoka for a Kyushu trip and searched for Fukuoka instead of Hakata. Looking at the price I nixed it without noticing the route was wrong. Now I know better, but I wasn't so used to things then.

I still haven't been to Kyushu!