Though the geisha culture is not as widespread as it once was, there are still many true geisha working in Japan. But the world of the geisha is typically reserved for the rich and well-connected in Japanese society. Geisha tearooms only cater to existing customers, so you can't just walk in off the street to be entertained by geisha.
Your best option is to head to Kyoto, and ask at the larger hotels if they have any connections with the local geisha houses. Many do, and can arrange for a geisha performance. Some places you might want to try include the Kyoto Gion Hatanaka, Hotel Centnovum, Hotel Nikko Princess or the Kamishichiken Beer Garden.
The Gion district in Kyoto is one of the busiest areas in Japan for geisha, and you can take walking tours to see the geisha houses. If you're lucky, you can see geisha in their full kimono walking between their party engagements. Just remember that these women are working, and they are not there to entertain tourists on the street.
If you're not heading to Kyoto, you can find geisha districts in Atami, Kanazawa and Niigata. Tokyo also has areas where geisha services can be found, such as in Shingashi.
