I've rented a car from Avis in Korea, but I did it in person at a
local office in Jeju. The transaction was pretty confusing as the guy
didn't speak any English and I never figured out the actual pricing.
The bottom line was acceptable, though. The car ran on LPG and as I
only had it for a day I didn't have to learn how to refill it.

You need an International Driving License to rent a car there.

Driving in Seoul would be difficult--like driving in Tokyo or New York
City--and I don't know why you'd want to as the subway is one of the
best in the world. Driving in rural areas (at least in Jeju) was
very easy.

Please post how the rental worked out once your return! I am interested in renting a car for weekend trips during my 4 week teaching position there this summer.

Having traveled in Korea several times--I really think it should not be a major problem driving. One tool that might help is to use a GPS unit. If they offer one with the rental, I suggest you take it. But...if you are comfortable with map reading and stopping often to ask questions, I think you should be ok. Korean drivers seem to be much more rational than drivers in some of the other Asian countries. I won't even get on a bicycle in Vietnam....basically because I don't want to die! But Korea drivers and roads are much better and I wouldn't hesitate to drive there.

Hope it goes well and again. please report back!