I must honestly say that for me my must see destination in Japan was not Kyoto, but Tokyo. but after some time researching about interesting places, I must say that Kyoto is top of my list, and it deserves to be there. There are several things that you ultimately will think of when you think of Kyoto, these things are old Japanese castles and temples -of which I think your head must have some imaginations of- and ultimately Geishas, who are the definition of Mysteriousness.
But before we go into all that, lets re-route from the beginning.
The common gate an average tourist such as me take to enter kyoto is from its main station -Kyoto station or in Japanese, Kyoto Eki -, and what you will see from that place is everything you don't want to expect from Kyoto -modernity-. The station was designed purposely to greet people to the new and modern Kyoto, and I think it really does serve its purpose, it was a wake up call from this perfect image you had of this city-at least for me-.
After arriving in Kyoto there are some things I immediately realised, the good news is that this city is very tourist friendly, it has packages for cheap mass transportation -you can choose a one day ticket for bus which is 500 Y , and you can use any bus inside the city for a day, or you can choose the one or two day ultimate package for train and bus, each 1200 Y and 2000 Y, with the ultimate package you will get discounts on several tourist destinations, but of course rules imply- which is simply very convenient, also there are buses that purposely go to the biggest tourist attraction, so everything is very convenient. but the downfall of this is that Kyoto is the second most expensive city in Japan -after Tokyo-, which makes this city very expensive. Food here costs around 700 Y minimum, of course if you choose fast food and conbini food (Japanese for convenient store) you can still eat bellow 500 Y, but restaurants I tell you are super expensive.
Now lets talk tourist destination, the number one tourist destination is Kinkakuji, which is the golden temple, I think pretty much everyone thinks of this place when they think of Kyoto. The second one I think is either Gion -the old town full of mysterious Geishas- or Kyumizudera. I think these three are the must see in Kyoto. but don't get me wrong, they are not necessarily the best ones.
Kyoto is the city of thousand temples, I don't know if this is true or not but I know that there are a lot of temples, and that 4-5 days will not be enough to see all of them -I am talking with experience because I did spend 4-5 days there-. My friend whom I stayed with during my visit to Kyoto has even been in Kyoto for one and half years and she hasn't seen everything, so please put that thought away. you will ruin your stay there if you keep insisting on seeing everything.
So my advice is what everyone should do on any journey, do some research. the 3 most famous spots I mentioned earlier are not necessarily the ones that suits you the most. I must admit though that I didn't do much homework until a day before my trip to kyoto, and mostly I read every information in the shinkansen from my city to Kyoto (which was a 5 hour train), so I didn't know much either, but the 3 places I mentioned earlier were the ones I already had in mind.
If you are like me, not having enough time to research than please when you reach Kyoto, go to the Tourist Information centre in Kyoto Eki, there you must ask about the coming events, and maybe you might get some enlightenment.
One thing about Japanese people that I admire is their lust to illuminate everything during what they think are special occasions. These include the fall season (Aki), Christmas Holidays,Sakura season etc -Japanese people love to celebrate-. there are places which look best in each season and they will illuminate these certain places accordingly, so please ask the kind man/woman in the information centre whether there are some illuminations during your stay or not.
Another thing you must research for is which place is best for what season, because what I have also come to learn about Japanese people is that their idea of a beautiful place is sometimes or many times integrated with its surrounding -landscape design-, which will make one place better in what season. And it really does truly make a difference.
Kyoto is particularly famous for housing the best Aki season and Sakura season in Japan, so if you have a great longing to experience the true Japanese taste, its only natural for you to come on these seasons. Ofcourse summer and winter have their own exquisite beauty.