Dec 27-31 � Hiroshima
Dec 27
Travel to Hiroshima and Stay in Hotel
Dec 28
Hiroshima Peace Memorial Museum
1-2 Nakajima-cho. Naka-ku, Hiroshima, Hiroshima Prefecture
Dec 29
Setoda Town
Seto Inland Sea, Hiroshima, Hiroshima Prefecture
Hijiyama Park
Hijiyama Koen, Hiroshima, Hiroshima Prefecture
Dec 30
Mitaki Temple
411 Mitakiyama, Nishi-ku, Hiroshima, Hiroshima Prefecture
Hiroshima Castle
21-1 Moto-machi, Hiroshima, Hiroshima Prefecture
Dec 31
Atomic Tomb Dome
1-10 Otemachi Naka-ku, Hiroshima, Hiroshima Prefecture
Shimizu Gekijo Theater (if time permits)
2-1-5 Matoba-cho Minami-ku, Shimizu Kanko Building, Hiroshima, Hiroshima Prefecture
Jan 1-4 � Nagasaki
Jan 1
Travel to Nagasaki and Stay in Hotel
Jan 2
Nagasaki Atomic Bomb Museum
7-8 Hirano-machi, Nagaski, Nagasaki Prefecture
Jan 3
Mount Inasa
Inasamachi, Nagasaki, Nagasaki Prefecture
Jan 4
Shinchi Chinatown
12-7 Shinchimachi, Nagasaki, Nagasaki Prefecture
Confucius Shrine and Museum of Chinese History
10-36 Ouramachi, Nagasaki, Nagasaki Prefecture
Jan 5-11 Tokyo
Jan 5
Travel to Tokyo and Stay in Hotel
Jan 6
Akihabara � Sightseeing
Akihabara, Taito, Tokyo
Jan 7
Senzokuike Park
2-14-5 Mainamisenzoku, Ota, Tokyo Prefecture
Jan 8
Anamori Inari Shrine
5-2-7 Haneda, Ota, Tokyo Prefecture
Jan 9
The Tsukiji Market
5-2-1 Tsukiji, Chuo, Tokyo Prefecture
Tsukiji Jogaii Market
Tsukiji, Chou, Tokyo Prefecture
Jan 10
Shinjuku � Sightseeing
Shinjuku, Tokyo Prefecture
Jan 11-14 � Osaka
Jan 11
Arrive and Stay in Hotel in Osaka
Jan 12
Dotonbori � Sightseeing
Dotonbori, Chuo-ku, Osaka, Osaka Prefecture
Jan 13
Shinsaibashi � Sightseeing
Shinsaibashi, Osaka, Osaka Prefecture
Jan 14
Fly back Home
It's a rather slow-paced trip but that will allow you to be flexible.
You plan to visit the Atomic Bomb Dome on a separate day as the Peace Museum but the dome is right there in Peace Park, so you should visit the dome and peace park on the same day as the museum (Dec 28). That leaves Dec. 31 open aside from the theater.
Are you going to Miyajima? I notice on the 27th your only plan is to get to Hiroshima. You can make good use of that day to see something. If not Mijajima, maybe try stopping somewhere along the way from Kansai to Hiroshima, such as Okayama. Korakuen Garden does not close during that time and it's one of the top gardens in Japan. Also the shrines and sites in the Kibiji District will be open.
I don't know about opening times for other places so you'll have to check but other ideas of places to stop along the way:
-Kurashiki
-Onomichi
- Kure (you seem interested in WWII sites, so this is a good addition very close to Hiroshima city:
http://members.virtualtourist.com/m/a40e1/edc96/
