Hi Martha,
Yes, what Daniel suggestions were great, if you just want the easy way. If you willing to take the challenge to properly plan your trip, you can save up the Yen$12,600/- as I think 14 days will be good.
If you are coming from Narita Airport, you don`t really need to JR pass if you are not in a hurry/rush:-
http://www.japan-guide.com/e/e2027.html
By JR Narita Express
Direct, 60 minutes, 1500-3140 yen, 1-2 connections per hour
The most comfortable way of travel between Narita Airport and Tokyo Station is the JR Narita Express (NEX). The one way journey takes roughly one hour, costs around 3000 yen and is fully covered by the Japan Rail Pass and JR East Pass. There are departures every 30 to 60 minutes.
With the Suica & NEX package, available for 3500 yen to foreign tourists only, you can travel by Narita Express from the airport to Tokyo and receive a Suica prepaid card worth 2000 yen (500 yen refundable deposit plus 1500 yen worth in train fares). A round trip version is available for 5500 yen.
By JR Sobu Line
Direct, 90 minutes, 1280 yen, 1 connection per hour
The JR Sobu Line (Rapid Service) is the slower but cheaper JR alternative to the Narita Express. The one way trip takes roughly 90 minutes, costs 1280 yen and is fully covered by the Japan Rail Pass and JR East Pass. There is about one departure per hour.
My suggestions, would be go to combine your stay in Tokyo first, where you can adjust to the cultures and places after your long travel from you country. You should leave one or 2 days to stay in Tokyo before leaving to repack your luggages/bags (with gifts)
You can visit Hakone without the JR Pass, as you can get the Hakone free Pass:-
The Hakone Free Pass by Odakyu Railways is a special pass for exploring Hakone, and includes:
Please check the website: http://www.japan-guide.com/e/e2358_008.html
Then, you can start to use your JR Pass to the places that are far -down south, and then travel your way up North again with the JR Pass.
JR Pass also cover the JR Bus express to Okayama, or Shikoku (night bus too: can save up on accomodation)
Naoshima (near the Naoshima (直島)[1] is an island located in the Seto Inland Sea of Japan.)
http://wikitravel.org/en/Naoshima
To go to Naoshima, you can go to Okayama by JR Pass-the Sanyo Shinkasen to Uno, as describe below:-
By Boat
Naoshima can be reached by boat from Uno (Honshu) and from Takamatsu (Shikoku). Naoshima has three ports, Miyanoura, Honmura and Seto port. Most services go to Miyanoura.
Miyanoura port — Regular ferry services runs about 13 times a day from Uno (20 minutes, ¥280) and about 5 times from Takamatsu (one hour, ¥510). Passenger boat run twice daily from Uno (15 minutes, ¥280) and High-speed boat once daily from Takamatsu (30 minutes, ¥1200). Passenger boat is for passengers only.
Honmura port. Passenger boat also run from Uno to Honmura five times a day (20 minutes, ¥280).
Seto port. Ferry boat runs from Uno six times a day (15 minutes, ¥220). There are some services for only vehicles.
Train
From Okayama, a stop on the San'yo shinkansen, there are infrequent local trains directly to Uno (65 minutes). Otherwise, take the Marine Liner rapid train and transfer at Chayamachi (茶屋町) for the train to Uno (40 minutes with a good connection). The train cost is ¥570.
After your trip from Okayama, you can go to Hiroshima, Kobe, Osaka, Kyoto, then travel all the way north to Tokyo. With the JR Pass valid for the last 2 days in Tokyo, you can then plan to go to Nikko, check:-
http://wikitravel.org/en/Nikko
The last day to Airport can be a bit tiring, and usually you want to get there early to shop around the Narita airport, and get ready to go home, guess the JR Pass is still important with the Narita Express. If not you could get a direct express bus from Shinjuku or pick up from certain hotels in Tokyo which cost you about Yen$3000/- or less.
All the best, do have a pleasant and safe journey....
