Kyoto is generally a very safe city for women travellers, though it's best not to be lulled into a false sense of security by Japan's image as one of the world's safest countries. Women travellers are occasionally subjected to some form of verbal harassment or prying questions in Japan, so take the normal precautions you would in your home country.
The Hankyū and Keihan line commuter trains in Kyoto have women-only cars to protect female passengers from chikan (men who grope women and girls on packed trains). These cars are usually available during rush-hour periods on weekdays on busy urban lines. There are signs (usually pink in colour) on the platform indicating where to board, and the cars themselves are usually labelled in pink in both Japanese and English.