Seogwipo is spread out in a thin line along the coast from Seogwipo downtown to the east and Jungmun to the west along the main arterial road, Ilju-ro Highway #1132.
By bus
Like it's northern counterpart, Jeju City, Seogwipo has its own inner-city shinnae bus system. Almost all of the buses take the same route along the highway between downtown and Jungmun, but tend to branch out at either end, servicing even a few of the smaller villages such as Daeepyeong-ri in the south-west of the island. In the downtown district there are a pair of bus "terminals" located around a main traffic roundabout from which most depart downtown, else just make your way to the highway. Inner-city buses cost 1000 won.
Long distance inter-city buses mostly follow the same route along the highway as inner-city ones and can also be used to get around. The cost is a little higher but they are faster, only stopping at major locations before zipping out of town to Jeju City. These long distance buses look more like tour buses than the city buses and go pretty much anyhere on Jeju. Seogwipo has two inter-city terminals. The main inter-city terminal is in the south-east of downtown, near the Jeongbang Waterfall. The second is to the right of the E-mart in front of the World Cup Stadium tucked in the back of a rather nondescript building. In practicality however, you can get just get on from one of the larger bus stops on either side of the highway around the stadium or Jungmun, and or at the traffic roundabout in downtown.
By Motorcycyle
There are one or two places that rent scooters in Seogwipo.
On foot
The main city area of Seogwipo, World Cup Stadium and Jungmun all lie in a 25-30km long thin strip along the coast. Whilst it is downright easy to wander each of the three key areas individually, walking between them would be inconvenient. Having said that, the Jeju Olle hiking trails do run along the coast in this region.
Most places can be comfortably walked to from the nearest highway stop.
By taxi
Taxis are also an option and most places are happy to call one for you. However, if planning to go the full 25 km distance from Jungmun to downtown, you may find the bill a bit steep.