If you want to witness geisha perform and then actually speak with them, one of the best opportunities is at Gion Hatanaka, a Gion ryokan that offers a regularly scheduled evening of elegant Kyoto kaiseki (Japanese haute cuisine) and personal entertainment by real Kyoto geiko (fully fledged geisha) as well as maiko (apprentice geisha). Children under seven years are not permitted.
Check the website for the schedule; Friday-night performances are guaranteed but other nights are subject to change.