Hello,
I'd say the itinerary looks pretty solid, rather brisk but that may be the way you like it. For Hakone, you might look into a Hakone Free Pass. For Kanazawa, be sure to go see Kenrokuen, which is regarded by many as the finest traditional historic landscape garden in the country. Near Kyoto, if you haven't been there before and you can squeeze it in, visiting HImeji Castle, which is Japan's finest, is very worthwhile.
For a day trip to Hiroshima/Miyajima, it is possible if you start very early - you can cover the best places in Hiroshima City (Peace Park/Museum, castle, Shukkeien Garden) and spend about ¾ of a day to see Miyajima.
For Miyajima, please note that there are 2 ferry companies there - make sure you go to the JR one if you want to use your pass. Also well worth seeing just beyond Miyajima is Iwakuni with its iconic historical bridge and mountaintop castle. Akiyoshido is a superb and largely unknown gem and one of the few times where you can ride a JR bus using your pass. It's about an hour's ride from Yamaguchi Station. It can actually get quite humid inside, so you might bring some bottled water. Be aware though that natually there are no restrooms inside the cave. Be sure to take a moment and walk through the karst formations (Akiyoshidai) above ground. If you have time, you could also visit
Hagi which is delightful, and the preserved samurai district and Mori-clan related temples and cemetery a rarity.
For Fukuoka, don't miss the Nanzoin Temple which is one of Japan's finest and virtually unknown to the world. You can see this site as a good guide. Look into a Fukuoka Tourist City Pass also. The Tochoji Great Buddha is there too and the biggest wooden Buddha in the country (30 tonnes).
Nagasaki is really the most interesting city on the island. It is worth a couple days to see the city. Dejima is really quite a historic site, and while only a few stones of the original foundation are still there, many of the buildings have been recreated and you might be surprised to see a few familiar things there. If you really want to be amazed, go see Huis Ten Bosch which looks like a Dutch village just pulled out of Holland and plopped into Japan. It's mostly scenery, but you will definitely feel some Déjà vu.
In Nagasaki be sure to go see Mt. Inasa at night if the weather is clear, and try the Nagasaki chanpon and saraudon! Also the Koshibyo temple is an often overlooked shrine that is quite unique in Japan. If you go see the Peace Park in Hiroshima, you could skip the one in Nagasaki if you are short of time.
Best of luck.