Kyoto is very easy to get around on the buses and trains. Buy a 1 day bus pass (see photo) and bus map; board buses at the back and exit at the front. A proposed itinerary would be:

Day 1 - Golden temple, Ninna Ji and surrounding area, followed by lunch at Otsuka (fantastic Wagyu beef). Then walk around that area - great cherry blossom and bamboo forest. Then get the train to Kyoto station and on to Fushimi Inari.
Day 2 - Do the Castle and Imperial palace followed by Soba lunch at 500 year old restaurant - Honke Owariya. Then head to Heian Shrine and do the philosophers Walk up to the Silver Pavilion.
Day 3 - Shopping near Gion (Nishiki Market Teramachi and Shyin Kogokyo), then lunch at Okonomiyaki (savoury pancake). In the afternoon, more temples (Kiyomizu-dera, Yasaka shrine) and then in the evening grab a beer at the entrance to Maruyama Park, followed by Geisha spotting in Gion.