Plan Seoul by neighborhood, not by attraction count.
For a first visit, the easiest way to protect usable travel time is to group nearby areas into the same day.
A simple first-time structure
With three days, focus on central Seoul and one modern district. With four or five days, add more neighborhoods without turning every day into a cross-city commute.
Gyeongbokgung area, Bukchon or nearby traditional neighborhoods, then Insadong or Jongno.
Myeongdong, Namsan area and central shopping or food districts.
Hongdae, Yeonnam and nearby café or nightlife areas.
Gangnam, COEX area or another southern district if it matches your interests.
Use it for missed sights, shopping, a slow neighborhood day or an easy day trip rather than forcing another long transfer.
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