if you can make below journey within 7day, then the pass is cheaper than purchasing the individual tickets although you need to take Hikari instead of Nozomi.

Single ticket price
Tokyo – Kyoto: JPY13,320 by Nozomi
Kyoto – Nara: JPY690 x 2 by JR Nara
Kyoto – Hiroshima: JPY10,890 by Nozomi
Hiroshima – Osaka: JPY9,950 by Nozomi and JR rapid service
Osaka – Kansai airport: JPY1,160 by JR Kansai Airport Rapid Service

Total: JPY36,700

Although we recommend you to stay in Kyoto for few nights as there is so many beautiful sites to visit… but yes, the day trip is possible if you are on a tight schedule.

Sample train schedule,

Outbound

08:03	Tokyo
[164min]	Shinkansen HIKARI 463
10:47	Kyoto

 

Inbound

19:29	Kyoto
[164min]	Shinkansen HIKARI 534
22:10	Tokyo

On my recent trip to Japan I made lots of day trip by Shinkansen (bullet train) and other JR with 7day Japan rail pass and it was absolutely a great value for money!

I activated 7 day-ordinary pass at Narita on 04Nov and used following route.
( There are local train between Omiya-Tokyo, but as changing to Shinkansen is easier, so I just pop on Shinkansen rather than normal train.)

04Nov: ¥3,680
From Narita to Ikebukuro by Narita Express -¥3,110
From Ikebukuro to Minamifuruya by JR local train – ¥570

05Nov: ¥23,820
Minamifuruya - Omiya by JR local train – ¥230x 2 = ¥460
Omiya – Kanazawa ¥11,680 x 2 = ¥23,360

06Nov: ¥3900
Minamifuruya-Omiya by JR local train –¥ 230 x 2 = ¥460
Omiya – Tokyo - ¥1,580 x 2 = ¥3,160
Omiya – Toro - ¥140 x2 = ¥280

07Nov: ¥28,910
Minamifuruya-Omiya by JR local train -¥230
Omiya – Tokyo -¥1,580
Tokyo – Shin Osaka -¥13,550 x 2 = ¥27,100

08Nov: ¥22,570
Tokyo – Nagoya -¥10,380 x 2 = ¥20,760
Tokyo – Omiya - ¥1,580
Omiya – Minamifuruya by JR local train: ¥230

09Nov: ¥360
Minamifuruya-Kawagoe by JR local train: 180yen x 2 = ¥360

The total cost for single tickets will be ¥83,240 but I paid only ¥23,800 for 7day ordinary pass!!

It depends how much you will travel within the pass validity but for my case it’s definitely worth to buy a pass!

The JR Pass does cover the basic fare, however it does not cover the room fare and express charge.

Extra express surcharge: 3,150 yen (between Osaka or Shin-Osaka or Kyoto and any stations in Hokkaido)

‘Mizuho’ is unfortunately not covered by Japan rail pass, its same as ‘Nozomi’.

But you can take ‘Hikari’, ‘Kodama’ and ‘Sakura’ bullet train using Japan rail pass.

For example,
From Shin-Osaka to Hakata (Fukuoka): take Hikari or Sakura
From Hakata to Oita: take Sakura or Tsubame and change to Limited Express Sonic at Kokura (or direct to Oita by Sonic. Its depends on the time you travel)

You can take a ‘Hikari’ or ‘Kodama’. Hikari is the fastest service on that route covered by Japan rail pass. Hikari stops at few more stations so it will take slightly longer than Nozomi. Kodama stops at all stations

Here is the individual tickets price for your itinerary.

Day1: Fukuoka (Hakata) to Kumamoto: ¥5,190
Day2: Kumamoto to Aso (return): ¥4,360
Day3: Kumamoto to Yufuin: ¥7,360
Day4: Yufuin to Fukuoka (Hakata): ¥4,430
Day5: Fukuoka (Hakata) to Hiroshima: ¥8,900
Day6: Hiroshima to Kyoto: ¥10,990
Day7: explore Kyoto
Day8: Kyoto to Nara (return): ¥1,380
Day9: Kyoto to Kanazawa: ¥6,910
Day10: Kanazawa
Day11: Kanazawa to Osaka: ¥7,640
Day12: Osaka to Kansai airport: ¥1,160

Total Price: ¥58,320

All the above route are covered by 14day Japan rail pass: ¥45,100.
Please note you can only exchange your pass at JR Hakata station and need to purchase the single ticket from Fukuoka airport to JR Hakata station which will cost you ¥250.

JR West Rail Pass (Kansai) (1-4day) but its not valid on Shinkansen though.

JPY9750 per single (£68-appox) and 4 day Sanyo pass is ¥20,000 (at the moment £138). The fare is almost the same but you are able to make other journeys within 4 days with Sanyo pass.

You can use your rail pass up to JR Odawara station. If you wish to go to Hakoneyumoto station, take a private rail from Odawara, will only cost about £3.00 (17mins).