I didn't know that Korea has Kilometre Zero (도로원표 道路元標) as well, until I visited Daegu (대구 大邱). Before this, I have heard of London Stone and the Kilometre Zero of Japan at 日本橋 in 東京. So, I give it a try to track down Kilometre Zero for Busan and its neighbouring city of Yangsan and Gimhae to check whether these cities have a Kilometre Zero as well.
But the marking stone might not be the actual point, as the case for Seoul, Daegu and Busan. Below the marking stone in Daegu, they stated where the actual point is, and so did Busan. At Seoul's, it is located 151m away; Daegu actual point is 215m away and located right in the middle of a main thoroughfare. Busan actual spot for Kilometer Zero is even further away, 9.74km from the marking stone.
I'm not too sure whether they have specific guideline on where to setup such marking stone, but as far as I know, they usually located near to city hall or town council. I have to remind you that near might be at some unexpected spot or unsuspecting location. There might be exception as well. Daegu's marking stone is not near to city hall but at Gyeongsang-gamyeong Park, which is the former Gyeongsang Provincial Governor’s Office. Maybe for historic reason the marking stone was placed there.
Usually for Kilometre Zero in Korea, they will provide the distance from the spot to various cities around Korea. I will provide some information on where I found the Kilometre Zero I have visited.
Yangsan 양산 梁山
Yangsan's Kilometre Zero is located at 남부동 남부사거리 front of a S-Oil petrol station, near to Yangsan's City Hall. It is on a junction between 시청로, 남부로 and 남부1길. If you refer to the map below, it is at the lower triangle traffic island. Click on the map for sky view.
Daegu 대구 大邱
As mentioned previously Daegu's Kilometre Zero is at Gyeongsang-gamyeong Park, in front of a post office. It is located at 중구 경상감영길, which is fairly straight forward as it is on tourist map as well.
Busan 부산 釜山
Busan's Kilometre Zero is located behind Busan City Hall, and if you walk pass the car park, you will see a park with a lighthouse. As you walk from the car park, you will see it as it is right in the middle of the path from the car park to the light house.
Gimhae 김해 金海
I've been to Gimhae twice just to locate Kilometre Zero. Only on the second attempt I managed to find it. Gimhae's marking stone does not have clear indication of the name of the city, just plain simple. It is located next to the guard house of vehicle registration office (차량등록사무소 車輛登錄事務所), by the crossroad of Gimhae City Hall. If you refer to the map below, it is at 시청사거리.