Short answer
Start with the season you want, then scale the route. Seoul is the simplest first base. Around a week, adding Busan can work; at 10–12 days, Jeju becomes a more realistic additional layer. Gyeongju is the culture-focused alternative rather than an automatic extra stop.
In this guide
First choose the travel season
The easiest broad windows are April–May and October–early November for comfortable sightseeing and outdoor time.
Spring is strongest for blossoms and palace/park walks. Autumn is strongest for foliage and mountain scenery. Summer works better when beaches or Jeju are central. Winter earns its place when snow, ski areas, winter food and city atmosphere matter.
Exact blossom and foliage dates move each year, so the framework matters more than a fixed calendar date.
Then scale the route
Short trip: Seoul first
For a short first trip, keep the route centred on Seoul. This is a qualitative choice, without a precise short-trip day cutoff.
Around a week: Seoul + Busan
Seoul + Busan can work for around a week, with 7 days as the more explicit planning marker for adding Busan.
This is a national overview, not a detailed Seoul–Busan allocation. Make the more specific two-city pacing decision separately.
10–12 days: Jeju becomes more defensible
At 10–12 days, Jeju can be added. This does not mean every 10-day Korea trip should include Jeju; it means the extra transport step becomes more realistic when the trip is long enough.
Culture-first alternative: Gyeongju
Gyeongju is the main culture-focused alternative. Use it when heritage and temples matter more than adding another big city or island.
Keep transport as a constraint, not the organising topic
Distinguish subway travel in Seoul, KTX between major cities and domestic flights for Jeju. These are broad route choices, not a fixed set of current services.
The route decision stays primary: how many regions are worth adding for the trip length and season?
Final decision
For a first Korea trip, start with Seoul. Add Busan around a week when coast and city contrast matter. Add Jeju at 10–12 days only when nature and island travel justify the extra move. Use Gyeongju when culture is the stronger extension.