Kyoto's Gion: Home to Geisha and Maiko
If you really do want to have an experience with a geisha or maiko, here are some basic details. Let me stress that there is absolutely no sex involved in this of any kind - geisha and maiko have never been prostitutes.
Gion Corner has two cultural shows daily by real maiko, though it's in a theater setting so you probably won't get to interact with them. It's only 3150 yen (cheaper if you can find a coupon online). Shows are at 18:00 and 19:00. The theater is located at the end of Hanami-koji.
Gion is best combined with Yasaka Shrine, Maruyama Park, Higashiyama, and Kiyomizu-dera. Ambitious tourists can also add Shorenin and Chionin temples. All of these sites fit into an active but manageable day for me.