abmj-jr has given you a great summary of the attractions of Kyoto, but I'll just add two notes.

First, don't be disappointed by your first glimpse of the city. Large parts of it are very modern, and it's the individual neighborhoods that hold the charm. That being said, Kyoto Station is a sight in itself.

Second, if you want to see maiko, go to Pontocho along the Kamo river in the evening. There are a lot of traditional-style entertainment establishments there, precisely the ones that send for maiko to entertain the customers. You can tell the maiko from the full-fledged geisha (known as geiko in Kyoto) by their hair or wig styles. The maiko have the hair on the top of their heads pulled straight back with a part on either side and the side hair pulled down at a slight angle, while the full-fledged geisha have all their hair pulled straight back.