Itinerary help

I live in Fukuoka-ken but I am still pretty new to Japan.

My parents and brother will be visiting May 7-24. Please look over our itinerary and comment on whether or not we should give or take time in certain places.

I am thinking about cutting out Fukuoka city and making Kokura a day trip from where I live in Buzen, that way we dont have to move our luggage.

Day 1-3 Buzen arrive and enjoy surrounding areas onsens and eating, day trips
Day 4-5 Beppu (overnight) onsen eating sightseeing
Day 5-6 Fukuoka(overnight) sightseeing/ eating- inexpensive hotel?
Considering Nagasaki
Day 6-7 travel to Hiroshima stay possible overnight or probably overnight in Miyajima island
Day 8-9 Osaka
Day 10 -13 Kyoto
Day 14?Takayama
Day 15 Nikko or Hakone (overnight or day trip from tokyo)
Day 16-19 Tokyo departure time 4:30pm

A couple of ideas:

In Beppu, stay at the Suginoi Hotel - they have a good variety of onsen and a fantastic meal/banquet plan. Rooms include dual western/Japanese rooms. (Transfer by free shuttle bus from the station).

Getting to Nagasaki from Beppu takes a while - I have stayed at the "Richmond" before, and that was nice. For Fukuoka we stayed at Hotel Forza (for the sumo) and it was close to the station (under USD200/night for a busy week).

For Osaka/Kyoto, pick one and day trip to the other - saves an extra hotel change. Personal preference is Kyoto. A day trip to Nara is easily doable from either.

Nikko - probably an organised bus tour day trip - very easy.