Hi,
A 14 day pass would pay off very well for you.
Although you might find that 3 days is more than enough for Naoshima - you might consider some other nearby places as well. Okayama is not far and it is famous for its castle, plus Korakuen Garden, one of Japan's Top 3, and also the Handayama Garden. If you'd like to get off the beaten trail for a while, the half day hike up to Konpirasan in Kotohira is stunning. Going to Takamatsu is also nice - it has one of Japan's finest gardens also, called Ritsurin.
Hiroshima also has a number of good places. Miyajima is the most famous, and aside from Hiroshima itself, Onomichi with its temple tour and Kosanji Temple is spectacular. Just beyond Miyajima also lies Iwakuni with its historical bridge and mountaintop castle. Taikodani is also a beautiful shrine in Tsuwano, Shimane. Hagi Castle was actually delightful, and the preserved samurai district and Mori Clan related temples a rarity. One of the very best places nearby is the Akiyoshi Limestone Cave, a 300 million year old wonder with huge caverns and underground river running through it.
Please also be aware that Hiroshima to Narita takes over 6 hours.