If you decide to spend a decent amount of time in Kyoto - and it's definitely worth it - I recommend you hire a bike, or buy one second-hand (usually a few shops near the university and they are very cheap). Kyoto is generally very flat and laid out in a grid structure so it’s dead easy to get around and you won't need to use the subway. Everybody cycles on the pavement as well so no need to worry about traffic. If you're there during the Japanese holiday season the main attractions are busy during the day - especially the Gion area. Best to go early in the morning - and it’s worth visiting Sanjusangen-do, Ryoan-ji, Daisen-in etc, even if they are busy (though I wouldn't bother with Heian Jingu)
Other recomendations include the area surrounding and including Ginkaku-ji and Honen-in (which is free) You can always walk back to the city via the Philosophers path.
I could go on for ages but a couple of other places I loved whilst there include Ippodo, a tea shop on the Teramachi dori, where they will explain in great detail how to drink your tea and for something less traditional there is Cafe Independants, in the covered Teramachi arcade, which is a bit more western and atracts a younger crowd. There is also a brilliant CD shop tucked away in the corner selling all sorts of Japanese avant-garde CDs(with some jazz thrown in) - if you're into that sort of thing.
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