If it's your first time in Kyoto, I would not stay at the Aman on a 4 night itinerary due to the location. If you plan to spend the majority of your time at the hotel and eat most of your meals there, it could be fine. Otherwise, I would choose a hotel in the middle of the city such as the RC or FS as you've mentioned. There is also the Park Hyatt and Mitsui.

The sights in Kyoto are spread out throughout the city. But when I stayed at the Park Hyatt, I would enjoy walking to the temples in the area and walking around the general vicinity. I could walk to Gion or pontocho for dinner and if I had to take a cab somewhere, it wouldn't be more than 10 or 15 minutes away. Same with the RC. I would enjoy walking along the Kamogawa river in the evening to have dinner and then walking back. On the other hand, the Aman seemed remote in comparison. There is Kinkakuji and Ryoanji nearby but there are almost no restaurants around other than at the hotels in the immediate vicinity. I stayed at the Aman last Fall and had a good experience. I spent 5 nights in Kyoto and spent the last 2 nights at the Aman. It was my 5th visit to Kyoto in the past 5 years so I was much more inclined to relax on the property than see many sights. It was a good fit for that purpose.