Itinerary check help appreciated

Hi,

Please help review and advise on transportation for my intended travel plan below. I would really appreciate your help. I intend to travel to Japan from 26/3 to 8/4 (14 days). I prefer staying in big cities for several days rather than visiting each city each day because I want to experience the normal life in Japan :).

Date Plan
26/3 Vietnam (SGN) fly to Osaka
27/3-28/3 Osaka
29/3 Osaka to Kyoto and back to Osaka
30/3 Osaka to Hiroshima, back to Osaka and Osaka to Kagoshima
31/3 Kagoshima fly to Sapporo
1/4 Hokkaido
2/4 Sapporo fly to Tokyo
3/4 Tokyo to Hakone and back to Tokyo
4/4 Tokyo to Fuji mount, back to Tokyo
5/4-7/4 Tokyo
8/4 Tokyo fly back to Vietnam (SGN)

Please help check whether my plan is OK and advise the most convenient and cheapest way (train or airplane) for the trips between Osaka-Kyoto-Hiroshima-Kagoshima, Tokyo-around Tokyo. For the trips Kagoshima-Sapporo and Sapporo-Tokyo, I intend to go by airplane.
Thank you very much.
Ms. Linh.