Hi. I'm thinking of doing my 3rd trip to Japan next October.
Previously, I have visited, with comments and good advise from this forum, Japan' biggest cities (Tokyo, Kyoto, Osaka, Fukuoka, Sapporo, Hiroshima, Nagasaki) and some significant spots (Nikko, Kamakura, Nara, Beppu, Hakodate, Takayama, Shirakawa-go, Koyasan, etc.). (2 trips/20 days each)

I'm starting to build my itinerary. I'm thinking of visiting Tokohu region (5-6 days, Sendai-Matsushima, Hiraizumi --according to previous Japan Forum threads-- Kakunodate, Nyuto onsen area) and center-south Kyushu (4-5 days. Kumamoto, Mt Aso), maybe passing through Kanazawa when going south.

Just in case I could add more days to my trip, I want to ask you some heterogeneous questions (my head is confused, I'm sorry):
-After reading a Korea trip report by jpatokal, I'm thinking of spending some days in Korea. I don't know if it's easy to re-entry Japan in case I take the ferry Fukuoka-Busan (I'm national of Spain, eligible for a visa exemption). In that case, I'd prefer to take the ferry instead of flying to Korea.
-As my return flight will leave from Tokyo-Narita and the closer I have seen Mt Fuji is from Shinkanshen line, maybe I could do a Hakone tour. I have browsed Sunrise Tours website, which offers a day-trip to Hakone. Is it a good option or it's better to go on my own, with a Free Pass?

Of course, I'd like to consider any suggestion about places to see (I've read several forum threads) in Tokohu and Kyushu.
Please, feel free to add confusion!

Thanks!