travel query

we will be in japan for about 2 weeks and wish to stay in tokyo for a few days, then on to Akita for about 5 days, then back to Kyoto before taking the ferry from Osaka. What is the most economical way of doing this? Buying individual tickets on train or weekly ticket or what? thanks

I assume that you enter Japan through Tokyo.

The best ticket would be a 7-day Japan Rail Pass to cover your trip from Tokyo to Akita and from Akita to Kyoto:
http://www.japan-guide.com/e/e2361.html

Alternatively, you could consider an air pass:
http://www.japan-guide.com/e/e2364.html