Seoul is dense enough that most visitors never leave it, which is reasonable for four days and a mistake for a week. Inside two hours of the city there is an eighteenth century walled city you can walk around on top of its own wall, an island covered in tree tunnels that Korean television made famous, the most heavily militarised border on earth with a viewing platform on it, and a port Chinatown where a noodle dish was invented. They are not equally worth your time.
The six options
Suwon, an hour on the metro, for a UNESCO listed fortress wall and a palace inside it.
The DMZ, north of the city, through an authorised tour only, with a passport.
Nami Island and Gapyeong, about two hours out, for tree avenues, a garden and a rail bike.
Incheon, on the metro, for Chinatown, colonial era streets and noodle history.
Yongin, for the largest theme park in the country.
Chuncheon, for a lake town and the spicy chicken dish that comes from there.
How to choose
One substantial sight: Suwon.
Something you will talk about afterwards: the DMZ.
Scenery and photographs: Gapyeong and Nami Island.
Food and history: Incheon.
Children: Yongin.
A weekday, in every case, because Korean weekends fill these places completely.

Getting to each
Suwon: metro line one or a suburban train, about an hour, no planning required.
Incheon: metro line one to Chinatown, about an hour and a quarter.
Gapyeong: train from Seoul, then a local bus or taxi to each sight.
The DMZ: tour coach from central Seoul, booked in advance, passport required.
Yongin: shuttle bus or metro plus bus, about an hour and a half.
Chuncheon: train from Seoul, about an hour and a half, direct.
Practical notes
A transport card covers the metro and the local buses on all of these.
Weekdays rather than weekends, without exception.
Cash is rarely needed; cards work almost everywhere.
Autumn weekends at Gapyeong and Nami Island are the single busiest combination.
The DMZ has a dress code and identity checks; follow what the operator tells you.
Download the local map apps before you go, because international mapping is limited here.
Where this fits in a Seoul trip
One day trip on a four night visit, two on a week, and not more than that.
For the city itself and how the districts fit together, our guide to Seoul covers the ground.
For the best of these options in detail, our guide to Suwon and the Hwaseong fortress covers the wall walk.
And for the one that needs booking and a passport, our DMZ tour guide covers what to expect.

The short version
Take Suwon if you want one substantial sight and no planning, the DMZ if you want the trip you will describe to people at home, and Gapyeong if you want photographs. Go on a weekday, because these are Korean weekend destinations first. Use the metro for Suwon and Incheon and a shuttle tour for Gapyeong, where the sights are spread out. Book the DMZ through an authorised operator, take your passport, and confirm what is actually open on your date.
