My idea of whirlwind train tour of Jpn:
(almost all trains are limited expresses / shinkansen)
day 1: fly to Wakkanai
day 2: Wakkanai 6.36a -> Sapporo 11.55a [lunch in Sapporo] Sapporo 14.38 -> Noboribetsu 15.54 [spend the night at onsen in Noboribetsu]
day 3: Noboribetsu 10.43a -> Hakodate 13.23p [hang out in Hakodate] Hakodate 15.45p -> Tokyo 21.23 [spend the night at Tokyo Sta Hotel]
day 4: Tokyo 9.20a -> Kanazawa 11.54 [hang out in Kanazawa] Kanazawa 15.19 -> Shin Kobe 18.26 [Kobe Ropeway / Herb Garden / dinner] Shin Kobe 21.15 -> Takamatsu 23.10 [spend night in Takamatsu]
day 5: Takamatsu 8.55 -> Nagasaki 13.51 [tour Nagasaki, spend night in Nagasaki]
day 6: Nagasaki 9.20 -> Kumamoto 11.48 [go see Aso] Kumamoto 18.01 -> Kagoshima 19.19 [spend night in Kagoshima]
day 7: fly back from Kagoshima