Don't waste your time driving in Seoul, that could be dangerous and slow. I know plenty of people who have driven in Korea, but don't speak Korean. Most of them did however have some working knowledge of reading Korean characters. Specifically, city and tourist names. So that challenge would depend on how ambitious you feel.
I have never driven in Korea myself, with KTX rail and the relatively easy bus system. However, whenever I was in a car with another driver, I realized the road system is not too difficult, and many of the historical or natural sites are well signposted. Maps including tourist sites are also abundant at rest stops. If driving is extra stress, I would just use trains and buses. The duration of your stay will really determine how much WHS and TWHS you can visit. For example, I took a bus from Seoul to Andong, Seoul to Boeun, Seoul to Gyeongju, among many others. I've also taken KTX from Seoul to Busan, and been a passenger in a car for traversing much of Gangwon-do and Jeollanam-do provinces. There are so much options, and by no means are buses or trains limited ONLY connecting with Seoul.
No difficultly (accessible by metro rail Seoul)
Seoul City Wall
Fairly Easy, Bus from Seoul
Gongju, Buyeo, Iksan (Baekje Sites)
(Sites in Iksan are a bit more off the beaten track, I had to use a mix of taxis and local buses)
- Depending on when you travel to Korea, Mireuksaji Temple in Iksan may be the most interesting Baekje site, granted the restoration is complete. The current completion date falls sometime in 2016. Oldest and largest stone pagoda in Korea.
- If you have some time in Gongju, it might be logical to try to visit one of the Buddhist mountain temples nearby. Magoksa Temple is about a 40 - 60 minutes bus ride from Gongju.
Middle Difficulty Bus from Seoul to Haeina/Daegu
You may have to make Daegu. It takes nearly 3 hrs from Seoul, and it will take some time to visit since its at the entrance of a national park (Gayasan). Secondly, it may be worth considering using Daegu as a base to not only visit Haenisa, but also the Jisan-dong Tumuli park which is perhaps the most interesting Gaya site and a key part of the nomination. Both sites are relatively close to Daegu. Dodong Confucian Academy is apparently not far away either.
Middle Difficulty, Bus/Train Seoul to Suncheon 3.5 - 4 hours
- Suncheon Bay (wetland, part of the tidal flat nomination)
- Naganeupseong, Town and Village
- Traveling to Gochang only for the dolmens may not be fully worth the time and effort, they are interesting yes. But the dolmens are best paired with other historical or natural sites. The Hwasun Dolmen site is located relatively close to Naganeupseong and Suncheon. It might be possible to do all 3 relatively easy and throw in Unjusa Temple in as well (potential tentative nomination).
Middle Difficulty, Bus Seoul to Boeun 3 hrs
- Beopjusa Temple (buses do not drop you off here, but follow the hikers!)
- Samnyeon Sanseong (serial component of the mountain fortress nomination
(Fortress can be tricky to visit, I couldn't find the bus, I took a taxi)
I can't speak much for logistics to these locations, since they are part of my current travel plan when I return to Korea
Daegokcheon Stream Petroglyphs