Hi Lynette,
I would suggest a JR Pass for your travel. This because the JR East Pass is only valid for travel in the Tohoku region, which is mostly north of Tokyo. The JR East pass for instance does not cover travel to Osaka, Kyoto and Nagoya. Since you are traveling all the time I would suggest a 14 day JR Pass.
Here's a list of normal ticket prices to give you an idea of possible savings.
Tokyo to Aomori - 3 days ¥ 16,870
Aomori - Sendai - 2 days ¥ 10,900
Sendai - Osaka - 2 days ¥ 21,690
Osaka - Kyoto - 2 days ¥ 540
Kyoto - Nagoya - 1 day ¥ 5,640
Nagoya - Tokyo ¥ 10,780
For a total of ¥ 66,420 or ¥ 21,320 in savings as the 14 day JR Pass is ¥ 45,100. You would probably end up making a lot more savings though as the pass is also valid for local travel in Osaka and Tokyo, can be used for travel into Hokkaido and also covers travel to and from the airport.
Time wise I think it looks good for the most part, however visiting Sapporo may be to much! Getting there from Tokyo would take up most of your day and you would not have a lot of time for sightseeing. Possibly it would be better to stick to Tohoku and visit places around there such as Aomori, Hachinohe, Akita and Sendai.
Hope this helps!
Daniel