I have previously been in Seoul, where I worked as a guest researcher in a university. I noticed that in general, a typical Korean address has no street name, except in the downtown area where the street (가/街) or road (로/路) may be instead shown. Since your destination is in Seoul, you do not need to worry about the province matter, because it is considered as a special administrative region (특별시/特別市).
According to my understanding, the system works in the following way: the Seoul city is divided into a number of districts (구/区), and then into a number of sections named "dong" (동/洞). Inside a dong, it is divided into a number of sub-sections called "beon-ji" (번지/番地), and by providing the number, this particular address place is then located. If the destination is an apartment, then the apartment name, together with the apartment number "sil" (실/室), are additionally needed.
To ease the delivery, a postal code, given after the symbol of 우) [similar to 〒 in Japan system], with a format of xxx-xxx (where x represents a decimal digit), should also be written after the address.
Hence, a typical address in Seoul, Korea would have a format similar to the following (information shown in the square bracket [~] is for the case where destination is an apartment):
대한민국 서울(특별시) ○○구 □□동 ◇◇◇번지 [△△△아파트 ▽▽▽실] ☆☆☆귀하 에게 우) XXX-XXX
and its corresponding format in Japanese would probably be --
大韓民国 ソウル(特別市) ○○区 □□洞 ◇◇◇番地 [△△△アパート ▽▽▽室] ☆☆☆様/殿 へ 〒 XXX-XXX