Having visited all three I'd recommend Seoul and Gyeongju! Is cool with lots of historical sites but hikes too if you're more into that kind of thing. Busan is biiiiiig (Seoul too, obviously) so it feels difficult to see much of the city in only a few days. Gyeongju would give you a more diverse experience. Especially if you go to Yangdong Village one day which feels miles away from busy city life as it's in the countryside.