There are many different options for transportation in South Korea. I live in Bucheon, so I'm going to be talking from the perspective of someone who has only lived in a city.
1. Using your feet: walking, running, whatever. using yourself and nothing else to get to where your destination is. Where I live I could easily never need to leave the radius of an hour walk and find everything I need to meet my basic needs, sometimes even my not basic needs. There are 4 grocery stores, 3 parks, my work, electronics stores, a million restaurants, coffee shops, park events, city hall, memorials... tons of stuff. Even the bus station. In fact there are a lot of pedestrian walkways you can use too.
2. Rollerblading: I have seen a couple Korean's employing this method. One things I'll state is I don't think its a very good idea for Korea. The sidewalks everywhere I've gone in the cities have been bricks laid down with sand between them, they are all uneven, and so there isn't really a flat surface to roll on. Except the street. You never really want to be in the street though, there is no safe place. Sometimes on the pedestrian walkways there is this little mini-street they put in for motorbikes that I've seen people using.
3. Skateboarding: same problems as rollerblading.
4. Biking: Biking is actually a great way to get around. You can go even farther than walking, the uneven ground doesn't matter. In fact bikes are very common here, but... they don't seem to have a law. People bike on the sidewalks, in the streets, take shortcuts through buildings. I'm not joking. However there are risks with biking. 1: Bikes are stolen all the time in Korea, so make sure to lock yours up. 2. Going into the street, cars are not really watching out for you so you can easily get hit. 3. Pedestrians will not move for you a lot of the time. Bikes range in price for whatever you want.
5. Bus: For the bus there are two ways to pay. You can either pay per trip, or get what is called a T-money card and add money to it then it just deducts as you take trips. The T-money card actually gives you a discount, and then gives you another benefit of your fair transferring. Such as if you take the bus then move to the subway, your fair from the buss will still count towards the subway. If you just paid cash for the bus you have to buy a full subway ticket. Busses range in price. there are 3 busses, blue, green, and red. The blue and green are local busses and are cheaper.
I'm not going to write in the prices cause they can change. The Red bus goes between cities so is more expensive, so avoid it unless you are actually going to that other city. Busses are great and don't cost that much to use, but they have their risks. For one thing, I think all of the drivers are playing a game when they stop of "how many people can we make fall down". They also play this when they start. Also, they will stop in the middle of an intersection during a red light to let their passengers out before they pick up more people. So once you get off you aren't always in the safest of situations. They are also dangerous if you aren't on them because they go so close to the side of the road when they stop make sure when your walking to watch out for busses coming at you, they speed up. Now, using the card, remember you have to scan when you get on the bus AND when you get off. If you dont' scan when you get off it will charge you for the entire trip. which costs a lot. I don't know when busses start running, but I know they stop at midnight.
6. Subway: The subway is the way everyone uses to get around that doesn't have a car when they need to go far. There are express trains, and commuter trains that stop at every stop. It has detailed maps and schedules, so you can pretty much figure it out even if you don't know korean. However, there seems to be something I'm missing because even with all my careful planning sometimes I still manage to get on the wrong train. Hell, sometimes the KOREANS manage to get on the wrong train and they do read korean. (I'm actually getting better at reading but I still don't know what I'm reading means.) As far as I can tell the fair is always the same low price unless you are a senior citizen.
Now, there are risks. You will get lost eventually. Keep your eye on your map, and if you don't have a map you should download a train AP to your smart phone. If you don't have a smart phone put it on your ipod/ipod/kindle... you don't have any technology? And you don't have a map? ok, then look at the map thats right above the train door. Which means you can't sitdown. Seriously, get a map! Make sure you know the station names you are supposed to pass, and watch closely for your station. You might mistakenly get on an express train that passes your station by, and if you aren't watching you wouldn't notice till you are way past and have to turn around.
With the subway know that it's crowded. Imagine being in the most tightly packed elevator you have ever been in. Now double the amount of people. It isn't always, but it can get that bad. There is no more personal space. Most likely, you will not get to sit down. Be prepared for a battle of seats if there is an open seat or if one opens up. People may elbow you. People do not move for you, you have to kinda push them. People do not say anything like excuse me while pushing you, they just push. And that's just the train ride itself. Getting on and off the train is a race, people don't line up nicely. Also, finding out which train can be a little hard, especially transfers. look carefully to follow the numbers, and check the direction of the train, and the corresponding stations. Trains start running at about 5am I think, and the stop at midnight from what I've seen. I don't know the exact times, or if that varies on holiday's or anything.
Taxi: Taxi's are actually pretty cheap in korea. sometimes. There are taxi's, and black taxi's. Regular taxi's are cheaper, but they drive like madmen. They need more fairs so they will sometimes pick up multiple customers. They run a meter, I know it's like 3000 won (aprox $3us) for the 20 min ride I took once. The black taxi's are more expensive but offer a safer ride I hear. I'm too cheap to take one. I did have a 20,000 won ride that took like 50 min which also isn't bad down in Busan. However that guy ran through 7 red lights and almost hit a lot of people and was speeding the entire time.
You can run the meter, but sometimes they will agree to go for a set price and won't run the meter. If you do that, you know for sure what you are going to pay, but they are more likely to take risks to get rid of you faster and get new customers in there sooner for even more money. Now the taxi's official end at midnight, so anything after that is "off the meter" and the rates go way up for them to bring you home. So you can either pile people into the car to make it cheaper (which is also illegal you can only have 4 passengers in the taxi legally unless it's a special taxi), or wait out the night at a 24 hour department store until busses and trains start running again, or if you are close enough walk. Normally if you are out that late you've been partying at the club till 4 am anyway so it isn't much longer to just pass out/chill drunk at the coffee shop that's still open for people like you.
7. Motorbike: this is also very popular if you feel like you can survive driving in the city. Motorbikes seem to drive wherever they want. I've seen them drive down the pedestrian only pathways, to merge directly into traffic, then pull a u-turn and head the other way. However Korea drives on the right side of the road so if you wanted to risk your life on a motorbike it is highly maneuverable and can get you pretty far. The thing though is now you are talking a lot of money being put into your transportation. First you need to get a license, where you turn in your licensee from back home and take the test here. Or you could get an international driving license from your home country. Then you need to get the bike, which can range in price from used to new. Then you have maintenance cost, gas, and parking. They are small so you can often find free parking. I assume there must be some kind of insurance too.
8: Car: You are crazy. I think anyway. I see car's get in accidents all the time. They drive crazy over here, they aren't careful, no one on the road is. The road is a dangerous, scary place. People park everywhere, they have no problem parking you in. You have to keep your phone number displayed on your dashboard so that if you park someone in they can call you to move your car. This is arguably the most expensive way to travel. You need the license, have to get a car, insurance, gas, and then handle the repairs when people crash into you.
So that's what I've learned about transportation here in South Korean.
if you want to know more about getting a drivers license, I suggest going here:
Eat your Kimichi
If you want to know more about the T-money card ( really anything about visiting korea)
go here
