Higashi-Chaya-machi, across the Asano River. Kanazawa's most famous geisha district. Many of the tall narrow houses are still used as high-class entertainment, but the Shima House (¥400) is open for all to see, and is well worth the entry fee for a chance to experience its refined and elegant atmosphere. Quite a few of the buildings have been converted into speciality shops and teahouses (of the non-geisha variety), so poke around freely and don't miss out on a cup of tea and a Japanese sweet (¥500-1000). Behind this area is a temple district, and the roads between the main road and the mountain are a twisting labyrinth of narrow lanes perfect for exploring on foot.
Nishi-Chaya-machi. The "west" to Higashi's "east", this is another district of restored geisha houses. However, this is considerably smaller (and quieter) than Higashi, with effectively just a single street, and aside from the (free) information centre it's not possible to enter any of the houses.