Every city in Japan has famous restaurants and most have a well regarded ramen shop. Each area of Japan has it's own style of ramen usually. According to this excellent website on Ramen, Kyoto is "known for it's soft, straight, medium-sized noodles." I'm not sure how famous this shop is, but it was nearby where Yayoi and I met so we ate there. I think it is not too far from Kyoto Shiyakusho-mae 京都市役所前 station.