The nearest bus stop, Nanajo-senbon is located just within 1 minute walking distance from Hostel Ayame. From here you can take buses which go around Kyoto city every 5 minutes.
These buses take you to Kinkaku temple and Kitano-tenmangu without any transfers. From the bus stop Umekoji Koen Mae which is 3 minutes walk from Hostel Ayame, you can take buses for Kiyomizu temple and Gion.
From the nearest train station, JR Tanbagchi which is an 8 minute walk from Hostel Ayame, you can take the train for Arashiyama and get there in just about 10 minutes.
Given you can get to Kyoto station in 10 minutes by bus from those bus stations above, it helps you get to the other destinations in the Kansai area such as Osaka and Nara, and it is also useful for visiting Kanazawa and Tokyo by bullet train.
Especially, to Nara and Osaka, some guests travel there as a day trip and come back to stay at Hostel Ayame. Since it just takes about 30 minutes to get to Nara and Osaka from Kyoto station, it is an advantage to leave your luggage at Hostel Ayame so that you can more easily enjoy your trip to those locations.