Renting a car was a last minute decision on our part and thankfully Trazy was able to answer all my questions regarding my license and my lack of a credit card. (they answer only on weekdays tho) Although you're supposed to book one week ahead, they were able to help me book a car 5 days before.
For four people with 3 large luggages and 2 small luggages, a compact car was just enough (they provided us with a hyundai avante). The car itself was so smooth and easy to drive.
The people in the counter were friendly and helpful (even retrieving my bag which I left in the shuttle bus). Even though they said I didn't need a credit card to book the car, I felt judged by the counter girl that I didn't buy any insurance (which you can only buy through a credit card). So in the end, I bought insurance, but since I didn't have any credit card, they allowed us to use my friend's credit card. (In the sites, they tell you that the credit card is supposed to be owned by the driver but in this case I think they care more that the car has insurance). We bought the cheaper one and I was VERY careful the entire 3 days not to scratch the car. (spoiler alert: I didn't :)))
The only downside of the experience is during the pre-checking of the car. After retrieving your car, you're supposed to go to a nearby office to have your car checked on its current condition before you use it.
After a 30 second survey, the guy just gave us an "its okay" and a "contract" telling us how to return the car. I called him again asking him nicely to help us with the korean GPS. He looked at it for one second and went, "no english. *points at gate* exit there *leaves us*"... He didn't even attempt to help us. It's a good thing I already researched online on how to use the Korean GPS but I forgot the specific buttons to press. So I called him again telling him that I KNOW that I can just use the phone numbers to locate our destinations, we just needed help with the specific buttons. And that's when he pushed the buttons consecutively, *points at gate* "exit there". I feel like he just wanted us to leave ASAP.
Also it's a good thing I know how to read korean (as a kdrama fan), so eventually I was able to change the dashboard media board to english and we were able to enjoy music in the car.
After three days, we were able to consume 45,000 worth of gas. Returning the car was easy, although it was super traffic in Jeju City that night, it's a good thing we planned to return it in advance, we arrived just 30 minutes before our "deadline".
Renting a car was definitely worth it. I do think it's cheaper to rent a car through AJ-rent-a car's website (after the free sign up).