You can see regular fares, routes and schedules on Hyperdia. But be sure under "More Options" to deselect "Nozomi..." since you can't ride that on the Pass.
The best site by far is the Todaiji Great Buddha and is a must see place. Yoshikien is currently free for foreign passport holders on tourist visas or landing permits. You can see the sights in Nara Park is half a day if you don't linger too much.
Kyoto is the jewel of the country though, and worth a lot of your attention. Even Kyoto Station is worth exploring, and it is just a train station. After the temples of Kyoto or Nara close down around 5 PM, you can zip over to Osaka for the evening. At night the city comes alive and has some great places to see, such as Dotonbori, plus the night views from the Umeda Sky Bldg, and Abeno Harukas Bldg are wonderful.
In addition, there are other numerous great places you can visit in the area. 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 castle on top of the mountain. 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 is the Akiyoshi Limestone Cave, a 300 million year old wonder with huge caverns and underground river running through it.
All in all, a lot more to explore and enjoy.