You need to update Immigration of your new residence within two weeks of moving. You can update your residency location by visiting Immigration or a local government office, including city hall (시청, 市廳, sicheong), district office (구청, 區廳, gucheong), neighborhood office (동사무소, 洞事務所, dongsamuso –or– 주민센터, 住民센 터, jumin senteo), town office (읍사무소, 邑事務所, eupsamuso), or township office (면사 무소, 面事務所, myeonsamuso). Some community centers can also do this but not all, so ask your Center's admin to contact them ahead of time to confirm.
If you are trying to update your address more than two weeks after moving, you are in violation of Immigration law. In these cases, you are only allowed to update your address with Immigration. You will get a fine and only Immigration is allowed to deal with that situation. Additionally, if you are hoping to later get a F-2-7 “points-based visa”, you will now be minus one point towards the necessary 80.
To update your address, you’ll need documentation to prove your new address, which is typically the housing contract, and don't forget to bring your Residence Card as your new address will be printed on the rear side. The ink within these boxes can sometimes get rubbed off, so you might want to cover these words with clear tape, being careful not to cover the blank spaces which might get used in the future.
One of the benefits of having your address on the back of your ID card is you don’t need to remember your address written in Korean. This can make registering at a medical facility much easier. “First time here?” Instead of filling out the registration paper, you can give them your ID card as it has all the necessary information; not only for general patient registration, but for proving you have insurance as well.