JR Pass required?

Hi,

Would you recommend purchasing a JR Pass for the below itinerary?

18/12/14 - 25/12/14
Tokyo + Yokohama + Nikko or Kamakura

25/12/14 - 26/12/14
Tokyo to Kawaguchiko

26/12/14 - 29/12/14
Kawaguchiko to Osaka

29/12/14 - 2/1/15:
Osaka to Kyoto + Nara

2/1/15
Kyoto to Tokyo

A 7 day pass will pay off for a Tokyo - Kansai round trip.

Your itinerary is 2 weeks?
JR 14days pass will be higher budget than single ticket.
It is better that you select other railway like a below.
Tokyo to Nikko: Tobu
Tokyo to Kawaguchi: Express Bus or Fujikyu
Osaka to Nara: Kintetsu
http://www.tobu.co.jp/foreign/
http://e.fujikyu-railway.jp/
http://transportationjapan.weebly.com/

Thank you for your replies

Do those alternatives above take more time to travel from A to B?
We don't want to waste time on a slower service.

We also don't want to worry about purchasing tickets on the day and being the December period, we are worried there may not be available seating on the shinkansen.

I have read that it is very busy the first few days of the new year and we are travelling back from Kyoto to Tokyo on the 2/1/14.

Having or not having a JR Pass has no influence on available seating. There are no seats specially reserved for JR Pass holders, everyone uses the same seats.