I really want to travel to Japan, and since I am looking more to experience their culture I assume where I want to go, more specifically, is ‘Old Japan’. What places are the best to visit and to stay to experience their culture to the fullest (tea ceremonies, springs, etc.)?
As the guys above mentioned, Kyoto is the best place. What I recommend are,
[Arashiyama]
Recently we have discovered hot spring here. Then you can experience onsen in Arashiyama of Kyoto. Have you ever ridden in a jinrikisha or a rickshaw. You can ride in it here. But costs a lot, say, around 100$.
[Kinkaku-ji temple]
It’s a golden temple and very beautiful. It must impress you!
[Yasaka-jinjya shrine and Kiyomizu-dera temple]
Most visited area in Kyoto. You should walk from Yasaka-jinjya to Kiyomizu-dera and you can feel ancient Japan.
[Heian-jingu shrine]
It’s a very big shrine. You can see a Japanese garden here. And there are some museums around here.
[My home lol]
You could possibly visit my home. But I don’t speak English very well.lol
<<EDIT>>
I’ve forgotten to write the great place to visit in Kyoto. "Gion" is the best area for you. You can see ancient valuable houses and stores here. Do you know Geisha or Maiko? Take a look at the link below if not. You can see them here in Gion. And you can also experience Japanese traditional cultures such as wearing kimonos, tea ceremonies and watching Buyo.
Geisha – Wikipedia
http://en.wikipedia.org/wiki/Maiko
Buyo – Wikipedia
http://en.wikipedia.org/wiki/Buyo