Hello there,
A 7 day JR Pass can be a nice option if you can include Tokyo - Fuji - Kyoto - Tokyo within the 7 day validity period. You can use the JR Pass and Shinkansen easily reach Hakone via Odawara station. Admittedly, the JR Pass is not valid within Hakone but you can use it to Hakone and again for the Shinkansen from Odawara to Kyoto.
Both Fuji Five lakes and Hakone are nice visits. In general, I would advice visiting Hakone over Kawaguchiko and Fuji 5 lakes, this because there is much more to do in Hakone and it is fun to visit the area on a day when the weather is not so good too. While you would just be looking at some grey lakes and Fuji is nowhere to be seen on a bad day. Add to that much easier access to Hakone with the JR Pass and it is an easy pick (at least if you ask me).
The JR Pass is also a good choice if you are not fully sure yet what you want to do. You get unlimited travel and can hop go anywhere if the fancy takes you. Think of a side trip to Yokohama or Nikko from Tokyo, or Osaka, Himeji, Kobe or even Hiroshima from Osaka.
Hope this helps,
Daniel