During my Spring 2000 visit, I had popped into a healthy food restaurant called Obanzai which offered a buffet service for a fixed price. Most of the food was vegetarian so I was damn well happy.
To my pleasant surprise, over two years later, the restaurant is still going. When we got there, it wasn't long before closing time. Actually there was no-one else there and you can see above that Aki had no competition when selecting food from the buffet.
Kyoto is renowned for Buddhist dishes, shojin ryori, which are vegetarian although expensive. Obanzai isn't the cheapest, but it's cheaper than going for a full shojin ryori course. Be aware that there are some other good vegetarian targets. Try the diverse Cafe Peace, near Kyoto University to the North, or the mouth-wateringly good Kerala, a South Indian restaurant in central Kyoto. Although there are plenty of Italian restaurants, I suspect that Kerala may be the only Indian restaurant in Kyoto. This is in contrast with Tokyo, which has plenty of Indian places.