Dubbing itself the "Blue City", Geoje is not so much a city but an island -- Korea's second largest after Jeju in fact -- and a loose collection of villages and settlements scattered in coves around the coastline. The two largest of these are Okpo (옥포) on the east coast and Gohyeon (고현) on the west. Most of the tourist sites lie between these two settlements around, and just off, the southern coastline. The intercity bus terminal is in Gohyeon but services also run from the odd remote bus stop.
The key attraction of the island is its natural coastal beauty. Outside of the two cities it is a near-endless series of calm blue beached coves and sheer pine-forested grey cliffs overlooking the sea.
Geoje actually has a significant role in Korea's naval history. The coast of Okpo is the setting for one of Korea's greatest military victories over Japan, during early stages of the 1592-1598 Imjin War. United under Admiral Yi Sun-sin, Korean armor-plated turtleships successfully repelled Japanese attackers from taking the Jeolla region. Although this ultimately did not stop the war in its tracks, it did slow the invasion a little and provide a morale boost to the nation.
Today, Geoje is a shipbuilding powerhouse hosting both Samsung and DSME shipyards. Despite the large number of foreign residents employed to supervise these facilities and subsequent notably high foreign presence in Okpo and Gohyeon, English signage on the island varies between minimal and non-existant.
Prior to December 2010, access to Geoje was limited to ferries or over the one bridge connecting to the mainland at Tongyeong. With the completion of the dual bridges and tunnel that comprise the Busan-Geoje direct expressway link, access by both express bus and car has been made significantly faster and easier.
Buses leave approximately hourly from the Busan Seobu bus terminal and take 1 hour and 20 minutes to reach Okpo via the new bridge (in reality it's actually a bit shorter). Note that where the bus drops you off is often not where you can pick it up again. Services to Okpo for example will simply drop you at a local bus shelter outside the Geoje Museum from where you cannot return. To escape the island, you must make your way to the Gohyeon Intercity Bus Terminal to get to Busan. Alternately, the area around Windy Hill has an obscure intercity link to Masan that runs every 2 hours until 8 pm.
Intercity buses also still service Geoje from Masan via Tongyeong (and also Busan, although this route being now superceded is likely to be phased out) taking roughly 2 hours and 1 hour respectively.
The coast of Geoje is littered with ports. Public ferry services run from Busan to Okpo, but taking the expressway bus is likely a little faster.
Private cars can take the toll expressway from Busan to Geoje. One key advantage to this is that you can take a brief break at a rest stop constructed on a man-made peninsula besides the undersea tunnel, the view from here being stunning.
This is the ideal scenario and the transport of choice for Korean visitors. Daegeoje-ro (대거제로) is a highway that loops the island following the cliffs closely and offering near continual spectacular views of the ocean and coastline as well as passing by practically every attraction.
If in a group, hiring out a taxis could provide an alternative, but they are rarely seen outside of the designated stands.
Geoje has an extensive local "inner-city" (cough) bus service catering towards locals. For tourists, it is a disaster, plain and simple. There is no single service that takes the Daegeoje-ro around the entirety of the island. Instead, the island is divided into a bunch of color-coded regions matching up with number-coded buses (for example, 10-19 and a weak-green color represent greater Okpo and Jangseungpo). The catch here is that there is only one stop where adjacent service regions match up and it's not announced nor explictly signposted. And then if you do find it (it is almost never on Daegeoje-ro but instead on a small unmarked detour off the road) there may be more stops than there are sides of the road with no signage in English nor Korean pointing you towards which services your next region. Outside of the two cities, services simply stop at sundown, stranding you wherever you may be.
Full maps of the bus system in Korean exist on roughly every second bus stop. If you attempt to tackle the full system, try to pay attention to the colors first, then the individual numbers. The square is not where you are now but the Gohyeon Intercity Terminal.
The most important route is the number 11 anyway and this is a frequent (roughly every 15 minutes) service that passes through the major cities and Jangseungpo Port.
In theory, it should be possible to loop the island using the number 11 to pass through the two cities, then transferring on to a blue coded 50-series bus for the rest. In theory, communism works.
If you do manage to figure the system out, bus fees are 1100 won in cash, or 1000 won using a transport card. For foreign cards, Busan Mybi, Daegu cards and Daejeon Hankkumi are not accepted, but Seoul T-money is.
Many of the attractions of Geoje lie on smaller island and islets just off the coast so ferry usage is mandatory. Specifically, close vantage of Haegeumgang and access to Oedo and Camellia Islands require it.
Each port along the south coast hosts a different ferry company that service Haegeumgang and Oedo, however, even if just visiting Haegeumgang you will likely be railroaded into a 1.5 hour stopover at Oedo. What you cannot do is use the ferry to travel between coastal ports as you must leave Oedo with the same company with whom you arrived.
In practice, ferries departing from Jangseungpo Port are the most useful as this is a mere one bus away from Okpo (take the #11 to the Art Centre). Furthermore, access to Camellia Island appears possibly limited to this port.
With settlements spaced approximately 5-20 km apart, walking between individual attractions would mostly be a foolish endeavor. However, one can easily traverse Okpo and the nearby war memorial on foot (likely faster than bus in fact). Similarly, the area around Windy Hill on the peninsula leading up to Haegeumgang can be covered on foot with ease.
war memorial, shrine to adminal yi, naval museum
cliffs (near theme museum)
swim 2 swimming beaches, notes about buses and local settlements
6 local dishes
hotels, minbak, motels, jjimjil in okpo
tongyeong, busan, masan, jinju