Hi there!
Firstly, lets get your costs:
- Narita airport terminal 1 > Tokyo: ¥3140, (62mins, 79km)
- Tokyo > Kamakura: ¥2100, (47mins, 51km)
- Kamakura > Tokyo: ¥2100, (47mins, 51km)
- Tokyo > Odawara: ¥3840, (35mins, 83km)
- Odawara > Nagano: ¥9530, (160mins, 306km)
- Nagano > Kyoto: ¥10930, (228mins, 398km)
- Kyoto > Hiroshima: ¥10990, (109mins, 380km)
- Hiroshima > Hakata: ¥8900, (138mins, 280km)
- Hakata > Tokyo: ¥21920, (367mins, 1174km)
- Tokyo > Narita airport terminal 1: ¥3140, (58mins, 79km)
TOTAL: ¥75380 for 10 legs
Can you give me advice on my itinerary?
While Fukuoka is a nice city - unless you have something specific to go for, or are aiming to travel deeper into Kyushu, the tourist experience can be a little limited, especially if it's just one night. Maybe here rather than branching out to Fukuoka I'd recommend travelling to Takayama, or a night at an onsen like Kinosaki Onsen. It's around 3hrs from Osaka, but is a fantastic little town with many Onsen, a great atmosphere and routinely described as the best Onsen town in the area of Hyogo. Here's a good forum post with more, and you can also book many onsen online.
You will have a few travel heavy days, but as long as you're ok with these things, then you're going to see a lot of great things in Japan!
Does it make sense to stay in Tokyo a few days, do a 7 day pass and try to visit a lot of long distance places, and then come back to Tokyo for a few days?
Looking at your itinerary I'd say that you could do a 7 day pass plus a few extras tickets if you wanted to save a little over a 14 day rail pass by using the following itinerary:
- Narita Express to Tokyo + prepaid Metro card combo with the N'EX + Suica package (¥5,500 return)
-
Hakone Freepass, which will give you 2 days of return travel from Shinjuku over the entire Hakone area for ¥5000
- Starting the 7 day pass on the trip to Nagano with the following itinerary:
Day 1: to Nagano
Day 2: Nagano + Kyoto travel in evening
Day 3: Kyoto/Nara
Day 4: Osaka/Kyoto/Nara
Day 5: Hiroshima day trip
Day 6: to Kinosaki Onsen
Day 7: to Tokyo
Planning the day trips also means that you can always cut it out if you are feeling too rushed.
This way, your total travel costs will be:
¥28,300 + ¥5,500 + ¥5000 + ¥4300 (kamakura) = ¥43,000 slightly cheaper than a 14 day JR pass, plus you get the added benefits of the free pre-charged Tokyo metro card, and the Hakone freepass benefits while you are in Hakone.
Hope this helps!