Do we need a JR pass?

Our itinerary looks like this:

Tokyo 5 nights, Day trip to Zao on the 4th day, 2 nights in Yamounchi Snow Monkey area, down to Kyoto for 4 nights, 4 nights in Osaka with day trips to Kobe.

Would it be worth getting a 7 day JR pass and activating the day we go to Zao? or would it be easier to pay as we go?

Please help.

Thanks

Are you returning to Tokyo to fly out?

Would get the pass.

Assuming you are flying out of KIX.
7 day pass is worth it. You might want to maximize the pass for Kobe trip as well. You just need to rearrange your itinerary.

We will be flying out of Osaka, would this change anything?

Thanks so much for the advice!

No.
To take advantage of the pass , do the Kobe trip during the pass validity.
You could even tweak the itinerary, and use the pass to visit Hiroshima and Miyajima as well.

Tokyo to Yamagata is 11000 yen.

http://www.hyperdia.com/en/cgi/en/search.html?dep_node=TOKYO&arv_node=...

Yamagata to Tokyo to Nagano to Kyoto. In this section, I entered Omiya instead of Tokyo to see the base fare. The assumption is somewhat less than the actual fare since Omiya to Tokyo to Omiya fare is not calculated. Further getting off at Nagano will increase Shinkansen fare. 24880 yen.

http://www.hyperdia.com/en/cgi/en/search.html?dep_node=YAMAGATA&arv_no...