JRPass

Hi there!

My gut feeling is that it'll be a good idea to use a JR Pass for this (in general, anything over a return to Kyoto makes a 7 day JR Pass worthwhile), but lets take a look at your basic ticket costs and see how they compare against the 7 day pass cost (¥28,300):

1. Tokyo > Matsumoto: ¥6710, (170mins, 235km)
2. Matsumoto > Kyoto: ¥9680, (210mins, 335km)
3. Kyoto > Hakoneyumoto: ¥9680, (210mins, 335km)
4. Hakoneyumoto > Kamakura: ¥9680, (210mins, 335km)
5. Kamakura > Tokyo: ¥890, (58mins, 53km)

TOTAL: ¥36640 for 5 legs

As you can see the base cost of tickets for the travel you list is higher than a 7 day rail pass (which would net you savings of ¥8340). I can certainly recommend the Japan Rail Pass for your itinerary.

Hope this helps!