From Kyoto to Fujigoko

What is the fastest & most convenient way to get from Kyoto to Kawaguchiko Stn OR Fujisan Stn OR Shimoyoshida / Gekkouji Stn, without having a JR pass. Departure time approx 11 am.

The fastest and - in my opinion - most convenient option is to take a direct Hikari shinkansen from Kyoto to Mishima and then a direct bus from Mishima to Fujisan Station from where it is a short train or taxi ride to Shimoyoshida:
http://www.japan-guide.com/e/e6905.html?aFROM=2158_6900

Thanks Uji. What kind of buses ply between Mishima and Fujisan? And any idea of the journey duration, frequency as well as ticket costs?

It is explained in the link that I included in my initial response! Please follow it. For you convenience, here is a direct link to the bus details: http://www.japan-guide.com/bus/gotemba.html

We are traveling to Fujigoko all the way from Kyotango on the same day and our itinerary may be such that we will only have 10 mins between our train from Kyoto reaching Mishima at 3.57 pm and then catching the bus at 4.08 pm. Is this advisable? Or do you suggest another plan?

suggest catching an earlier train.