7 or 14 day pass?

Hi there!

Here are some thoughts for you:

day trip cover

The JR Pass would cover all of your day trips. If you decide to visit Kawaguchiko, the JR Pass will cover the majority of the travel to Otsuki. From here you'll need to use the non-JR Fujikyu lines up to Kawaguchiko itself which would be an additional cost.

JR Pass coverage in Tokyo, Kyoto and Osaka

The JR Pass would cover much travel within Tokyo (map of JR lines in Tokyo), and 'OK' cover within Osaka and Kyoto, though in all cities you should expect to buy some non-JR subway tickets as needed.

Spending longer in Osaka

I'm not very sure about this as it really depends on what you intend to see. If you have no specific plans, then I think you're spending enough time in Osaka, but could aim to also fit more time in Kyoto into your plans, and also add day trips to Hiroshima and Nara from either Kyoto or Osaka.

7 or 14 day?

A 7 day pass is ¥28,300 with a 14 day pass coming in ¥16,800 more at ¥45,100. You'll need to spend at least these amounts on JR tickets for the various rail passes to be worthwhile. Lets take a look at your projected costs for the legs you list:

1. Tokyo > Nikko: ¥5,630 (121mins, 150km)
2. Nikko > Tokyo: ¥5,630 (117mins, 150km)
3. Tokyo > Kamakura: ¥2,100 (47mins, 51km)
4. Kamakura > Tokyo: ¥890 (54mins, 53km)
5. Tokyo > Otsuki: ¥2,860 (85mins, 87km)
6. Otsuki > Tokyo: ¥2,860 (76mins, 87km)
7. Tokyo > Kyoto: ¥13,420 (164mins, 513km)
8. Kyoto > Osaka: ¥540 (28mins, 42km)
9. Osaka > Tokyo: ¥13,950 (194mins, 556km)

JR ticket cost: ¥47,880 for 9 legs

• 7 day Japan Rail Pass (¥28,300) saving: ¥19,580
• 14 day Japan Rail Pass (¥45,100) saving: ¥2,780

As you can see you'll make great savings with both passes. If you keep your plans as they are I think I recommend a 7 day pass, with your Nikko visit conducted on the 15th, and purchasing separate tickets for the rest. It would mean a tight schedule however, and would not give you any JR cover in Tokyo or flexibility to change your plans. If you think this is important then a 14 day pass will still save you money and will let you explore any other areas at will.

Hope this helps!