You can find taxis anywhere in Seoul. They are convenient but have two major disadvantages. Firstly, especially when it's raining or snowing, or during rush hour, Seoul traffic can be atrocious and your cab ride could be very very very slow. Seconldy, taking a cab is the most expensive way to get around the city.  However, the cost is much lower than with western countries and you don't need to tip.

For most people, it is advisable to use the subway for most of your transportation needs. You may be OK with buses but apart from airport limousine buses and other express buses, bus travel can be quite hard. All buses only have Korean signs and route tables, and you also need to know the code for the type of bus -is it blue, yellow, greeen or orange? Unless you know or are feeling adventurous, stick to the subway. However, if you are transporting two or more people and heavy luggage, taxis are probably your best option.

There are three types of taxis in Seoul:

 The first type is the Standard Taxi, mainly cream or silver, and orange in color.  The fare starts at 2400won then goes up depending on the distance traveled at high speeds and the time taken at slow speeds. Between midnight and 4 a.m. the price will be increased by 20%. 

The second type is the Deluxe Taxi, also known as Mobeom Taxis. These are black with a yellow sign on top. Their basic and additional fares are more expensive but they offer a higher standard of service, more passenger space, and do not have a late-night charge. This is a good idea if you are a businessman in a rush needing to get to the airport, but not advisable for regular tourists on a budget just trying to get around.

 The third option is a Jumbo Taxi.  These are 8-passenger vans great for a large group or passengers carrying several luggages.  Rates are the same as the Delxe Taxi but way cheaper than taking two Standard Taxis.

  Also it is a good idea to have the address shown to the driver written in Korean. Not all cab drivers understand English and can't read the English address.  However, most taxis are equipped with special free interpretation devices. If the cars do not have it, the drivers can use their own cell phones to call 017-200-3000 to get an interpretation. Just say "FREE INTERPRETATION" or point to the sticker on the window.

Some useful words and phrases for your cab ride:

"______-e deryeoda juseyo" = Please take 'me' to______

"oreunjjok" =  right

"wenjjok" = left

"jikjin" = go straight

"yogiso naeryo jushigessoyo" = Please drop 'me' off here. 

 

Rental cars are possible, but will cost you a lot of money. It is also hard for Americans to get used to the driving style in Korea, and it can sometimes be intimidating since lanes seem to be optional, red light running is rampant, horns are used more frequently than turn signals, and motorscooter riders are definitely suicidal especially the delivery guys who even drive along the pavement.  Oh yeah, and the cost of gas is extremely expensive.