Ten days in Kyoto

I leave in two days! Thought I had more time to plan but now the pressure is on. Will be staying in a machinami in central Kyoto. One day for the Miho Museum and one day for Nara. Can you suggest a non strenuous itinerary with what I should definitely do and see for the remaining 8 days using public transportation? Is there a suggested tour I can take at the start in order to orientate myself to the City?

I think you should try to see a little more of Kansai in 10 days. Take a trip to Himeji and soak in the hot bubbly at Arima Onsen.

In Kyoto, apart from the usual Kiyomizudera, Gingkakuji, Kinkakuji etc., take a 30 min train ride to Uji to see Byodoin. Also, while there check out the cuisine at Manpukuji temple. You have a nice window of time where you can enjoy a lot of Kyoto and Kansai without stressing yourself out.

By the way, don't forget to try the tako yaki and the crab niku by visiting Osaka. That city is not the cultural capital, but definitely is the gastronomical powerhouse of Japan.

Check this forum out, there is a lot of information and make your itinerary yourself based on the pace you like.

Bon Voyage.

For kyoto just pick out a few temples to visit
And for all locations do read up about the transportation system. At the locations do visit the local TICs office for maps.

I agree with all of the above. Seeing Uji and the Byodoin is a good idea, but also just walking in the area around the river is very pleasant on a nice day. Try some Ujicha, arguably the best in Japan. Fushimi Inari Shrine is great late in the afternoon.
Another trip might be to Horyuji to view the oldest wooden structures on earth - a quick 10 minute train from Nara. To get away almost completely, take the train (3 changes needed) to Taimadera in Taima. The only intact three story, two pagoda arrangement in Japan, and very ancient. It's also the birthplace of Sumo and there's a park there recognizing that. I envy your 10 days in Kyoto!