This was my first time hiking on the Baekdudaegan in a while, but it was also one of the most enjoyable hikes I've ever had. Sobaeksan is located more or less right in the heart of South Korea, on the border of North Chungcheong and North Gyeongsang provinces. However, I found it kind of inaccessible despite its popularity.
Sobaeksan is located closest to the city of Yeongju in North Gyeongsang province. However, the mountain is about 20-30 km from the city itself and the bus connections from the city are quite poor, with buses running between every 1 and 3 hours, making it easier to go from Yeongju to Seoul than from Yeongju to Sobaeksan. Your options, in the absence of a car, would be to either come early enough the day before to take a local bus to the mountain, or to just show up and take a taxi.
If you're interested in the Sobaeksan portion of the Baekdudaegan, it starts at the Gochiryeong pass in the west and goes to the Jungnyeong pass in the east, a hike of about 26 km. Both are comparatively hard to get to without a car, but Gochiryeong is extremely difficult to access, and there are no accommodations nearby. So, your options would be to either stay as close as possible in Jwaseong-ni and either hire a vehicle (most hotels or pensions there do this) or simply walk the 60-90 minutes to Gochiryeong.
Admittedly, I found it absurd to walk about an extra hour or two just to begin what was already about a 12 to 14-hour hike. So, I started from Yeonhwa village in Jwaseong-ni, about 30-minute taxi ride from Yeongju city, the last third of it on a concrete road that appears to double as a hiking trail, and the last few kilometres on an unpaved gravel road. If you want some quiet solitude, this is the place. While the accommodations were spartan and the taxi ride cost 30,000 won, the trail leading to Sobaeksan was literally in front of the pension.
The hike from Yeonhwa village up to the main ridge is, obviously, not actually part of the Baekdudaegan, but I didn't really care. It's 3 km from Yeonhwa village to the Yeonhwa Samgeori (three-way intersection), and it's a tough 3 km on a narrow, steep dirt trail that tests the muscles in your legs. From there, it's 5 km to Gungmangbong peak (1420 m), a comparatively easier walk that takes 2 hours or so, the same as the 3 km from Yeonhwa village.
From Gungmangbong peak, it's only another 3 km to the Birobong peak (1439 m). You can actually see one peak from the other unless the weather is awful, which wasn't the case at Gungmangbong, but rain, hail and thunder rolled in during the hour it took to walk to Birobong. Fortunately, by the time I got there, it had completely cleared up. Gungmangbong and the kilometre to the east of it are probably the most beautiful parts of the mountain. It's a flat trail at the top with azaleas in bloom, at least this past weekend, and comparatively few people. Contrast that with the rockier, emptier peak of Birobong, which seems to be eternally crowded with hikers (you can see them from Gungmangbong, actually).
The Baekdudaegan trail continues 11 km from Birobong to the Jungnyeong pass, but I was tired from having run a race before. Along with wanting to take a nap on the rocks and really take my time, I decided to follow the rest of the people down to the Samga parking lot from Birobong, a 5-kilometre walk that supposedly takes three hours but I finished in just one thanks to this route being mostly on stairways and concrete roads.
If you just want to get up to the top of Sobaeksan and back down, I guess the course from the Samga parking lot up to Birobong via the Birosa temple would be the shortest and easiest way to do it. It's also, however, very unremarkable, and the first half is really not that different from walking up any uphill road in Seoul. You could try going up from the Choamsa temple, which goes up to Gungmangbong, and then walk over to Birobong, a total of about 9-10 km that would take 4 hours one way. It wouldn't be bad to go down towards Samga-dong once you're tired, about a 6-hour hike in total without breaks.
I'll probably continue doing mountains on the Baekdudaegan, having done about 100 out of 735 km so far, but my next two trips into the mountains look like they'll be the Dinosaur Ridge on Seoraksan and a run along the northern half of the Bukhansan dullegil to finish up the portions I haven't done yet. There are better things to do on mountains than to complete a long line of them.