Hi,
I've been to Korea many times since years ago, always on business and leisure mixed. I didn't like it at first because I thought the people were aggressively rude (and some are)....but after I got to know them, I found them warm and pleasant.
October is the typhoon season on the northeastern coast of Asia (Hong Kong, Taiwan, China, Japan, Korea). Most of the time, all this translates to is some bumpiness on flights in that area. Sometimes (and you've really gotta be "lucky" to have this), you may get a bit more....

October is also the Autumn season where its cool, yet you won't need a jacket (except for going out in the evenings).
Hotels are VERY expensive (but then again, I usually stay at the Myeongdong area, which is downtown Seoul, where the most expensive Korean real estate is). Whatever you do, stay out of the 5-star hotels like Hilton, Hyatt, etc.....or else you'll go bankrupt before check-out time the next day. The only time I've been to a 'branded' hotel was when a friend took me to Hyatt for the buffet dinner. She had coupons for the buffet, so it was OK for me.

Getting around is not difficult because there are very established networks of buses and trains all over the city of Seoul.
Seoul is not a pretty city to me. Its grey, spread out, boring. I always felt that Seoul looks like a slightly less chaotic version of Taipei (if you've been to Taipei, you'll know what I mean). In fact, doing business with the Taiwanese and Koreans are the same....they're equally demanding and aggressive!

I don't think I will elaborate on the areas in Seoul to visit because you can find that in any tourist website, brochure or book. Myeongdong, Itaewon, Lotte World, blah blah blah. Outside Seoul, I think one place which would be interesting to visit is the DMZ (demilitarised zone) - the border between the two Koreas. Sadly, I've never been there.
Shopping is very expensive in the department stores. But roadside stalls can be cheaper than Bangkok (for accessories and t-shirts). I bought a Be The Reds soccer t-shirt for S$3 only (but maybe it was because the World Cup was over by then). I heard that many of the imitation goods (eg. handbags, etc.) sold in Bangkok are imported from Korea anyway.
Koreans have the reputation of generally being rude, rough and uncouth....and you may see some of that, especially on flights in and out of Korea. BUT.....Seoul is the only city where I've experienced 3 times in a single day where people came up to offer help by giving directions (I was walking around with a map, at times standing on the street trying to figure out those maps). I say that the best is to go with an open mind and judge for yourself. As for me, I actually quite like them once I got to know them. Lets face it, Singaporeans are not known to excel in the area of friendliness either....
I feel that there is a bit of xenophobia in Korea. Maybe its because they've always been quite a closed-up society, whacked left-right-centre by foreigners, by North Korea....occupied by Japan for decades and all. If you dress, behave and talk different, you may get people staring at you (especially the older ones). They are harmless and probably just curious. Just either ignore them or smile and nod at them. It happens in every country anyway.....including right here in Singapore.
The Korean culture is based on conservative Confucianism, which I feel they're still half submerged in. Many Koreans are learning Mandarin now, mainly due to the emergence of China (social and business reasons). The older ones all can read traditional written Mandarin by the way....its part of their education, even though they've got their own writing (invented by King Sejong).
The Korean language has many similarities with the Chinese languages too. If you break down the Korean words, this becomes quite obvious. Like kongju (princess).....leng mien (cold noodles)......hakseng (student)....pok-pok (

just kidding).
Korean food is spicy and good for me. Good restaurant food is expensive and elaborate (S$100 or more per person). Roadside restaurant (more like coffee shops) food is about the same price as our food courts. Roadside stalls sell the best food, at very low prices (S$1.50-2.00 for a bowl of rice cakes, or meat on skewers). If you don't speak Korean, you may have to pay more.....what I usually do is to wait and watch how much the guy before me pays, then I buy it after him.
One thing you'll never have is constipation in Korea. All kinds of spicy kimchi for every meal, spicy bibimbab, spicy fibre dishes of all types.......these all ensure that you'll keep going and going....
