I would also strongly recommend against renting a car unless you have a solid knowledge of Korean (written and spoken). English is used far less in Korea than in, say, Japan, so even in Seoul it can be hard to find someone who speaks English--once you get out into the countryside, I would not be surprised if street signs do not have English at all.

I think from a cost perspective your best bet may be to seek out organized bus tours to the various rural areas you want to visit. Unless you want to go somewhere that's exceptionally out of the way, you should be able to find various group tours that would take much of the stress out of the experience for you.