Hi Tim,
Here are some answers for you:
I also read that the JR pass does not work on the Tokaido, Sanyo and Kyushu Shinkansen lines which i thought were the trains to Kyoto?
The countrywide Japan Rail Pass available on jrpass.com is valid on all the shinkansen lines you list. The only exceptions are on the class of bullet train. JRPass holders are not able to use the Nozomi and Mizuho bullet trains. These are exactly the same type of trains as the normal bullet trains on these lines, but stop at slightly fewer stations. In practice, the Nozomi and Mizuho are only slightly faster than the other bullets (Hikari, Sakura, Kyushu & Kodama). Certainly for tourism purposes you won't find much difference. Perhaps you were looking at the validity for other types of rail pass?
I think a rail pass will only make sense for the first part of your trip as this is where the bulk of your long distance travel is. To work out if a 7 day Japan Rail Pass is worth it for this part, you need to spend over ¥28,300 on single JR tickets. Lets take a look at your itinerary:
- Narita airport terminal 1 > Tokyo: ¥2740, (62mins, 79km)
- Tokyo > Odawara: ¥3440, (35mins, 83km)
- Odawara > Kyoto: ¥11550, (161mins, 429km)
- Kyoto > Nara: ¥690, (49mins, 41km)
- Nara > Kyoto: ¥690, (46mins, 41km)
- Kyoto > Tokyo: ¥13020, (161mins, 513km)
TOTAL: ¥32130 for 6 legs
Based on these costs, it is worth buying a 7 day rail pass for the first week for a minimum saving of ¥3830. You will also have flexibility to change your plans should you want to during this phase of your trip. As you will have the JR pass both in Tokyo on the 23rd and the 28th, you could certainly make more use of it (for example, to Nikko, or the other day trip locations you mention). Here is a map of JR lines in Tokyo to help you plan.
For Hakone, from Odawara I recommend purchasing an Odakyu Hakone Freepass, discounted to ¥3900 as it's from Odawara, not Tokyo. This pass will give you free transport up and around the Hakone lakes area.
For the following week, I recommend you purchase separate tickets as needed.
Hope this helps!