I just got back from a few days on Jeju Island and I know it's sometimes difficult to get English information in Korea, so I wanted to add some info to what's in the LP in case anyone decides to hike either of these trails.
Both the trails were quite beautiful, however unfortunately the weather wasn't cooperating for me, and so it rained most of the time with low clouds. In clear weather, though, there are probably amazing views, so I'll do this hike again in the future. I started going up Yeongshil and then down Eorimok. From trailhead to trailhead it took me a little over 2.5 hours, but due to the weather I didn't stop much and went at a fairly good pace.
The bus travels along the 1100 road (so-called because it reaches an elevation of 1100 metres), but it actually travels along road #1139. It can be a little confusing because most of the roads on Jeju are 11##.
In Jeju City, I believe the bus starts at the intercity bus terminal (#39 on the Jeju-si map), but I'm not positive as I only took it from the south. After Jeju City, it stops near the Eorimok trailhead, which is a 10-15 minute walk up a side road from the bus stop. It then goes to Yeongshil and stops at the lower parking lot, which is probably a 30 minute walk below the trailhead. The bus then heads for Jungmun, but it doesn't go all the way to the resort area. The Jungmun bus stop is actually a few minutes on a different bus, or a 10-15 minute walk from the Jungmun resort area.
Most of the buses between Seogwipo and Jungmun run along road #1132. You want to get off at Jungmun Primary School (bus stops are announced in Korean and English, and sometimes in Japanese and Chinese as well), and from there the bus stop for Hallasan is less than 100 metres, just north of the rotary intersection (towards Seogwipo from the Primary School – look for the little bus shelter). There's a bus schedule at the bus stop, but it's only in Korean, so I'm including the times for anyone trying to plan their trip.
Jeju City / Eorimok / Yeongshil / Jungmun --- Jungmun / Yeongshil / Eorimok / Jeju City
06:30 07:04 07:19 07:40 --- 07:45 08:06 08:25 08:55
08:00 08:34 08:49 09:10 --- 09:15 09:36 09:55 10:25
09:00 09:34 09:49 10:10 --- 10:15 10:36 10:55 11:25
10:00 10:34 10:49 11:10 --- 11:15 11:36 11:55 12:25
11:00 11:34 11:49 12:10 --- 12:15 12:36 12:55 13:25
12:20 12:54 13:09 13:30 --- 13:35 13:56 14:15 14:45
13:40 14:14 14:29 14:50 --- 14:55 15:16 15:35 16:05
15:00 15:34 15:49 16:10 --- 16:15 16:36 16:55 17:25
16:00 16:34 16:49 17:10 --- 17:15 17:36 17:55 18:25
That's the schedule for April 1 to October 31. For November 1 to March 31, the schedule is the same as above, except the first and last trips are cancelled (leaving Jeju City at 06:30 and 16:00).
Note: the schedule is current as of September 2011, but I don't know how often they change it.
For anyone looking to extend the hike, you can go up one of these trails and then go down the Donnaeko Trail (or vice versa), which although it is not shown in the LP map, is on the south part of the mountain and connects at Witseoreum (#1 on the LP map). It looks like it would probably be a nice hike, however as far as I know, there's no public transportation to the trail head, so you'd be on your own getting back to town.
If you have any questions about any of this, please send me a pm.
Jason