Visitors to Seoul are very likely to encounter at least one of Seodaemun, Namdaemun or Dongdaemun. Even if their tour guide (human, printed or digital) doesn’t tell them, it’s probably possible to figure out that they are the original west great gate, south great gate and east great gate of Seoul. Seo, nam and dong, therefore, are west, south and east. Dae might be great or gate, and mun might be vice versa, but the head of any compound noun is more likely to be in the first or last position, and finding that Gwanghwamun is the main gate of Gyeongbokgung palace firmly points to mun as gate.
These actually have (or had, in the case of Seodaemun) official names, which are 돈의문 (don-ui-mun), 숭례문 (sung-nye-mun) and 흥인지문 (heung-in-ji-mun) respectively (which are also rendered in hanja (Chinese characters used in Korean), but tourists don’t have to worry about any of that). Seodaemun also refers to a gu (local government area), park and prison, Namdaemun to a market and Dongdaemun to a gu, market, former baseball stadium and design plaza (and I’m sure a lot else each). Bukdaemun (north great gate) (officially 숙정문 (suk-jeong-mun)) exists but is far less known, partly because it is perched in the mountains, a moderate hike from anywhere.
Close to Namdaemun is Namsan (south mountain) on which is N Seoul Tower. There is no Buksan, but rather Bukhansan (mountain to the north of the Han River (of which more later)). In fact, there are at least two other Namsans in South Korea, the better known one being south of Gyeongju. Seosan is a city in the west of South Korea, but it uses a different hanja for seo, so it probably doesn’t mean west mountain. There is a Dongsan near Chungju Lake but that doesn’t appear to be east of anything. (There may be more of each – Wikipedia’s list is clearly not exhaustive.) There are several Dongsan churches around the world, including one in Sydney. As far as I understand, the east mountain is where we can see the sun rise (literally or figuratively) (or, in Christian terms, the Son rise).
Eleven of South Korea’s cities have san in their name, including Seosan (above) and Busan. They all have the hanja for mountain (one of the few I actually know), but there may or may not be actual mountains named Seosan, Busan etc. Ansan the mountain in Gangwon and Ansan the city near Seoul are obviously unrelated and none of the other city sans have mountains with the same name (but were obviously named after a mountain at some time; maybe the mountain was renamed to avoid confusion).
You may be wondering if the seo of Seoul means west. It doesn’t. There’s some doubt as to what it does mean, but none that it doesn’t mean west. Apparently 서라벌 (seo-ra-beol) means capital city, and originally applied to Gyeongju during the Silla era.
Further south than Namsan is the Hangang, or Han River. Han has a number of meanings, the relevant one being large, great, the Han River dominating the middle part of the country. That gives two words for great: dae and han. Of the two, dae is more common and refers to a greater number of people, places and things, for example Sejong Daewang (Sejong Great King or (King) Sejong the Great), the cities of Daegu and Daejeon (note that Daejeon was previously named Hanbat), daehakgyo (university) and daero (highway). Seoul was previously named Hanseong, but that was fortress on the Han River rather than great fortress. Dae and han occur together in the official name for the Republic of Korea/South Korea, 대한민국 (dae-han min-guk), but that han has a slightly different meaning, coming from Samhan, the three great confederacies of the Proto-Three Kingdoms period (from the first century BCE) or the three kingdoms of the Three Kingdoms period. (This is not the same han as the Han dynasty of China or the modern-day Han Chinese ethnic group.) South Koreans more often use han-guk or especially when comparing South and North Korea nam-ham and buk-han respectively. Han is also found in hanbok (Korean clothes) and hangeul (Korean alphabet) and is hidden away in Hallasan (South Korea’s highest mountain) and hallyu (the Korean wave of popular culture). This can be seen from the hangeul 한라산 (han-la-san) and 한류 (han-ryu) respectively.
South of the river is the stylish Gangnam. Gangbuk is not immediately opposite it, but is in the north of the Seoul special city area, bordering Bukhansan National Park. Gangseo and Gangdong are at the west and east of the Seoul special city area, both to the south of the river. I have mentioned Bukhansan. There’s also a Namhansan, on which sits Namhansansong (south of the Han river mountain fortress) (and indeed a Bukhansanseong). Namhansan is more south-east of Seoul; south of Seoul is Gwanaksan.
Further afield are Seoadaejeon and Dongdaegu, both stations on the KTX network, and Donghae (east sea), Namhae (south sea) and Seohae (west sea), more commonly Hwanghae (yellow sea). There is, of course, no Bukhae (north sea).
There’s the east sea (Donghae) and the city of Donghae and the south sea (Namhae) and the island and county of Namhae, as well as another county named Haenam. Not to mention the 한려해상국립공원 (hal-lyeo-hae-sang-gung-nib-gong-won) and the 다도해해상국립공원 (da-do-hae-hae-sang-gung-nib-gong-won). Haesang means maritime and gungnib gongwon means national park, but I haven’t been able to find the meanings of the other parts. (Note the han in hallyeo.)
I am now approaching 1000 words, so will finish this post. One last point: in English, we say “north, south, east, west”. In Korean, they say “동서남북” (east, west, south, north), for reasons I haven’t found but which are probably related to the directions of the sun.
(I’m not going to link to all of those places. Search and you will find.)