Kyoto is about thirty minutes by train from Osaka, so many visitors day-trip from an Osaka base — but if you want the temples early in the morning, staying in Kyoto is far better. The JR Haruka reaches Kyoto Station from Kansai Airport in around eighty minutes, and the station gathers the shinkansen and the city buses, which makes it the safest area on a first visit.
Kyoto has few subway lines and leans on buses, which run badly late in peak season. That makes "is it on the way to the temples I want" often more useful than "is it near a station". Gion and Kawaramachi are easiest for dinner and an evening walk, while Arashiyama suits anyone who wants the bamboo grove before the crowds. Kyoto also has many ryokan-style stays where the meal plan moves the total considerably.
Rates peak hardest during the late-March to early-April blossoms and the mid-November to early-December foliage, when some hotels sell out half a year ahead. July, with Gion Matsuri, and Golden Week behave the same way. January to February and the June rains bring rates down and leave the temples quiet, which can suit a walking-and-photography trip better.
In Japan the total can change within the same hotel depending on the plan. Before booking, check whether breakfast is included, how the public bath is used, whether accommodation and bathing taxes are paid on site, and the free-cancellation deadline. Check-in is typically 15:00 and check-out 10:00-11:00, with early check-in usually chargeable. Rooms are often smaller than Korean travellers expect, so confirm the bed configuration and whether an extra bed is possible for three or more guests.
For two nights, base at Kyoto Station and split the days between the eastern side — Kiyomizu-dera and Gion — and the west at Arashiyama. With three nights or more, keep the first two near the station or Shijo and move to Arashiyama or Higashiyama for the last, so you can reach the temples early. When combining with Osaka, putting Kyoto first means less luggage shuffling.