I understand car rental GPS systems allow inputting a phone number instead of the address to look up a driving route. For Jeju, since a lot of the attractions are nature-oriented and may not have a phone number, how would this work?

English GPS systems seem to be a rare commodity from the car rental agencies, so I'm looking for an easy way to find my way around driving without being held back by the language barrier. I don't know how to input an address in Korean, so the phone number method is crucial. The places I would like to visit include :

Manjanggul Cave
Seongsan Ilchulbong Peak
Cheonjiyeon Falls
Oedolgae Rock
Jusangjeolli Cliff
Cheonjeyeon Falls (Yeomiji Botanical Garden)
Yongduam Rock
Sanbangsan
Sangumburi Crater (산굼부리)
Hallim Park (Ssangyonggul and Hyeopjaegul Caves)
Songaksan Mountain

The standard Korean GPS navigation systems in cars that you get at Herz or Avis are bi-lingual. They also feature a full text search, which was enough for us to find our way around Jeju last year.

The only problem we faced is that e.g. Hallim Park has several entrances and we were unsure which one to chose of the text search results. But, overall it works quite well.

Furthermore, there are plenty of tourist maps and brochures that feature GPS directions (such as phone numbers or numbers nearby) that help.

Unfortunately, my car rental is with Kumho and I could not even select a GPS device as part of my reservation.

Hertz licences KT (which is Kumho) at Jeju - that's where we got our car from. It's a short shuttle bus ride from the airport. The nav system was bi-lingual. And, I hope to remember correctly, the GPS rental in Jeju was free and in every car. Staff were very helpful, patiently explained the nav and helped to enter our first destination. The GPS is ok; nothing special and has its shortfalls - it was fine for us. (Trip was in Nov last year)

Avis is AJ (at least at ICN); their nav was the same, so also bi-lingual.

Another option is renting a Mifi at Jeju Airport (at least in Seoul very cheap) and use your cell phone to navigate. As you can pre-set routes and have internet in general, this might actually be convenient in any case.

Overall, navigating your way around Jeju is pretty easy and sights are clearly signposted on the road. Speed cameras are atrocious; cruise control is a nice feature to have in the car.

Perfect. Thanks for your insight!