Sandra

Hi,
Your plans make it a bit knotty to cover the pass. If you get a 7 day pass, then use it from Aug 15-21 to go Tokyo-Kyoto-Takayama-Tokyo, it would pay off quite nicely. There really is no need for 3 nights in Takayama. If you want to use a 14 day pass, then you'd need to expand your travel a bit. If while in Tokyo you took a day trip to Nikko, and while in Kansai, did a day trip from Kyoto to Himeji by bullet train, which has Japan's finest castle, you would cover the costs of a 14 day pass. You could also use it to go from or to Narita airport by the Narita Express which is very convenient (your trip is too long though for taking the Narita Express both ways on a 14 day pass, but you could also use a cheap 1000 yen bus one way).

Seeing Yokohama is fine, although the fare is not that high. You could combine a visit to there plus going to see another delightful place next to it, Kamakura/Enoshima.
As for seats, it is true that August is a busy season, but it is doubtful that the trains will all be so packed that you can't get a seat. There are trains leaving every 15 minutes or so, and you can also make seat reservations in the JR office ahead of time (and with no extra charge on a Pass). You might want a couple of seats on the right hand side to see Mt Fuji if the weather cooperates while going down to Kansai. However, if you still want to splurge for the Green Seats, you can do that of course.

Good luck!