backpacking trip

Hello all,
I'll be on a girly on a budget backpacking trip with a friend, in Japan.

Our ideia is to do:
Flying into Tokyo
- 8 days in tokyo (Including Universal Studios) -2 days in Mount Koya - 2 days in Kyoto -3 days in Osaka Flying out of Osaka

Should we get the Jr pass at all? if so, 7 or 14 days, since for most of the time, we will be in Tokyo?
Also, how does the transportation in tokyo city centre works? is there a unlimited 24hrs like pass.

Any trips are happily accepted.

Thank you vm