Tokyo - Nozawa Onsen - Kyoto - Hiroshima - Osaka

Hi there!

A 7 Day JR Pass would pay of if you could at least use it to cover the following:

Nozawa - Kyoto ¥ 11,460
Kyoto - Hiroshima ¥ 10,990
Hiroshima - Osaka ¥ 10,820

This would result in a total of ¥ 33,270 or ¥ 4,970 in savings. Remember that the more you add to more savings you would make. It would really be nice if you could include your trip Tokyo - Nozawa as well, saving an additional ¥ 8,900. I would suggest buying normal tickets for your arrival and first days in Tokyo as travel cost around the capital is low and the JR Pass is better used for longer distances.

As for staying in Tokyo, I personally love the Ueno/Nippori area, which is a little more relaxed than Shinjuku (and maybe a little saver too at night). Both places are right on the Yamanote line which offers direct access to many big stations in Tokyo, such as Shinjuku, Harajuku, Shibuya and so on. It is also easy to visit Asakusa from Ueno which is also romantic to visit at night.

I hope this helps!
Daniel