What qualities do you look for when you are looking for a holiday accommodation. If you are looking for a peaceful ocean view, great services with a spotless room, these two places should suit you well. Among many popular accommodations, these two places are quite hot and you need to book at least a couple of months in advance.
Jejurak is well known for its beatiful cafe(Cafe 7373) and 5 star hotel like rooms. It is especially popular among couples. Room rates go up to KRW190,000(about USD170) during peak summer holidays so please check out by sending e-mail mentioned in their website. http://jejurak.com/pages.php?p=7_1_1_1
The owner of Modern Pension is a well-known blogger among Jeju lovers. Her blog is about her life in Jeju as a Jeju immigrant.(Jeju immigrant is a new word for Koreans move to Jeju from the mainland because living is Jeju as non Jeju person is like living in a foreign country.) Unfortunately her interesting blog is in Korean but you can still book a room at her beautiful pension by e-mailing her at firstname.lastname@example.org. She speaks Chinese, Japanese and a bit of English. http://moderninjeju.com/index.php
Jejurak and Mordern are nearby. You can take a taxi from Seoguipo bus terminal or they are about 10 min walk from the nearest bus stop(Beophwan Elementry School).