Rail Pass considerations
A round trip to Kyoto on the Bullet Train will cost just over ¥26,000. As a 7 day pass comes in at ¥28,300, so I think as long as you do more travel, either on the JR around Tokyo, or to places further afield, the Rail Pass could be a good choice and would certainly give you more flexibility. All JR bullet trains have a mixture of reserved and non-reserved seating. With the Japan Rail Pass you are free to use both types of seating. Making a reservation normally costs money, but with a rail pass you get them for free and can make reservations easily and on the day at the normal ticket counter.
It seems like you have 2 main bases in mind, Tokyo and Kyoto.
You can easily get out to Yokohama, which is a lovely city and Nikko with its lovely temples. Having said that, I think you'll have your hands more than full just taking in the city!
I think there's much more scope to explore Japan around Kyoto with a Rail Pass.
In day trip territory, there is wonderful Nara, an hour away from Kyoto on the train, and Arashiyama which sits next to Kyoto with its lovely bamboo groves. You can also get down to Hiroshima and back easily in a day from Kyoto. If you're on a tight budget, the hotels Vista and Sunroute are budget friendly, modern and convenient and there is a good YHA youth hostel in the Higashiyama area of Kyoto.
For overnight stays away from Kyoto, I have 3 great trips:
I strongly recommend a trip to the [Art Island of Naoshima]. You can stay on the beach inside the gallery area in very reasonable heated mongolian tents. It's an amazing experience. You can also check my guide of [how to get to Naoshima with a Japan Rail Pass].
Takayama. Personally I prefer it to Hakone etc as it's a little off the beaten track (and therefore not tourist prices), and you get a wonderful taste of Japan up in the mountains. You can get to Takayama in 3 hours by train from Kyoto(http://goo.gl/mi1oW).
Kaga onsen kyo. A great little onsen (hot spring) area that is 2 hours away form Kyoto on the train. Wonderful hotspring baths that are, again, a little off the beaten track and therefore a little cheaper than most mainstream Onsen areas.
Hope this helps!