@kja do you have an easy link to your trip report to South Korea? I’d love to read it!

Here is a 'photo safari' I put together for some off-the-beaten-path places in Korea. I had a car for a week.

South Korea Photos

You can go off the beaten path without leaving Seoul or Busan. Both cities are enormous and cover mountainous territory well beyond the tourist sites. In Korea, where the cities end the mountains begin. There is no buffer zone.

If you want to explore food, you can't do better than going to a rural restaurant for duck, goat or unique versions of homemade tofu. These are very much associated with rural life and hiking, so you mostly won't find those things in urban environments. In my link, I describe a duck meal I had in a very remote location, but you can get to places in the mountains without really leaving the two biggest cities. If you want to know more about these places, let me know.

Oh that's a tough question!
Yeosu is a good choice if you love seafood, it's one of the best places to try soy-marinated raw crab, and braised cutlass fish, amongst other dishes. We also loved the fairly short bike rail there (these exist around SKorea so there are many others), and we did a day trip to Suncheon Wetlands as well.
Jeonju is super touristy but has specialities such as tteokgalbi, jokbal and bibimbap.
Suwon is known for its galbi!
We ate well throughout South Korea, to be honest!

Wow 4 weeks! You must’ve seen and eaten so much, now I’m jealous and hungry at the same time.

4 wonderful solo weeks in South Korea

Sorry -- just seeing your message now!
Let me know if you have questions. If you do, it would be best to add them to my TR.

BTW: If you click on someone's screen name, you can find all their TRs. Or you can use the search function to look for a particular poster's screen name.