Jeju is a very easy place to drive in! Just keep in mind the speed cameras that are all over Korea, but if you grab a Korean navigation app (Naver, Kakao) they'll tell you where all of them are.
Were you saying US$180 per day? I've rented for as low as $10-15 per day. I'm a Korean resident, so that may factor into some of the cheaper deals I got, but I've definitely seen deals for about $20-25.