Most Cost Efficient way to travel Japan 6-7 Days

For nearly all passes, you must have a Temporary Visitor Status in your passport (i.e.landing permit or tourist visa). People on student visas will not qualify. There are a few exceptions you might look at though, such as the JR Kanto Area Pass.

See:

http://www.japan-guide.com/e/e2357.html

For a good guide to various passes.

Flying on a low cost carrier is also a good possibility:

http://www.jetstar.com/jp/en/home

https://www.starflyer.jp/index.html

http://www.skymark.jp/en/

http://www.flypeach.com/home.aspx

http://www.vanilla-air.com/en/

Is there any Pass for going around Kyoto, Osaka, Hiroshima, Nara Area?

AFAIK, only the Koyasan World Heritage Ticket if you have a student visa.