There are sooo many things to see and do in Kyoto that even two years would not be enough to see everything! So what you will want to do is think about what you are most interested in. For me, I like to just wander around and find smaller less crowded places. That being said, there are some 'must see' sights. Just make sure to go there right at opening time or just before closing to get a bit of breathing room. One thing is for sure, pack comfortable shoes because you will be doing a lot of walking!
Suggested one day itinerary: East Side
9:00am Go to Heian Jingu Shrine
Suggested: by foot from Higashiyama Station
Where better to start your tour than at the Heian Shrine, which boasts an amazing classical Chinese style garden which would have been right at home in the Heian period (794-1159) a time when the privileged classes walk around in fine garments writing poetry and having incense parties. Just make sure to be first in the gate before the busses unload and you will feel like you have the place to yourself.
10:00am Go to GInkaku-Ji Temple (the Silver Pavilion)
Suggested: by taxi from Heian Jingu (700yen)
Less glamourous than Kinkaku-Ji (the Golden Pavilion) this temple was built by a famous shogun as a retirement home to be later made a Zen temple. The funny thing is the temple never received it's silver roof because of the outbreak of civil war in Kyoto. While the city burned and the rivers ran with blood, the shogun rested here and followed a lifestyle later to be know as Higashiyama Bunka which was heavily influenced by Zen and the Japanese concept of Wabi-Sabi (or beauty in simplicity and imperfection) The gardens here are stunning!
10:45am Walk the Tetsu-gaku-no-michi (Path of Philosophy)
This lovely walk was named in much more recent history for the two philosophers who loved to ramble along the lovely canal while waxing philosophy. There are several shrines and temples along the way. It is tempting to go to each one, but I normally just keep moving along till I get to Nanzen-Ji
11:15 Check out the Zen Garden at Nanzen-Ji temple or go up to the top of the gate and get a cool view of Kyoto.
12:00 Check out the Kyoto International Community Centre
This is a really lovely building with nice facilities with English speaking staff who love to help foreign guests. A lot of the services are for foreign residents but it is worth checking out even as a traveller.
12:30 Go eat some Okonomiyaki
Okonomiyaki is a well know "Kansai" area specialty which is sometimes described as "Japanese pizza" and there is a shop right around the corner from the International Centre which is very tasty and provides an English Menu.
4:30pm wander the streets of Gion. Great time for spotting Maiko and Geisha running off to dinner appointments
5:30pm Go to Kiyomizu Temple for an amazing sunset view.
Suggested: by taxi from Gion
6:00-6:45pm Walk from Kiyomizu Temple to Yasaka Jinja (great atmosphere at night through the cobble stone streets)
7:00pm Grab a drink at a friendly Irish pub Man in the Moon