I'm going on a close of service trip with another Peace Corps Volunteer from Africa starting in September, and we want to know where all we should visit in Thailand and South Korea.
We don't want to go to huge parties or be stuck in a crowded area the whole time, but are more interested in historical sites, beaches and anything outdoors like treks, wildlife, animals etc.
And also the average prices for these activities and how expensive it is to travel/eat/sleep in each area.
Here's my perspective on Korea (I've only been living here for 18 months & still need to see tons more!). I hope it helps / kickstarts your thinking.
Seoul, though crowded, is a must-see -- if only to give you an accurate idea of Korea as a land of contrasts: between super-connected, smartphone-addicted Korea & more traditional country towns (of which there are plenty!). While up there, you might want to check out the demilitarised zone (DMZ), but be sure to book in advance.
Busan is a beach city on the east coast.
Namhae County, incl. Namhae Island (which is absolutely beautiful!) & the Namhae German Village (not really touristy except during Oktober Fest, but still very interesting)
Jeju Island (southern-most Korean island):
semi-independent volcanic island, offering beaches, hiking (Hallasan Mountain -- highest in Korea, I think...), horse-riding and lovely scenery. (it won't be as humid in September, & the monsoon will have passed, so it should still be quite lush).
Jeollabuk-do Province (main city: Jeonju):
- The Hanok (i.e. traditional) Village in Jeonju. It's the only hanok village where people actually live.
Jeollanam-do Province (main city: Gwangju):
- Jirisan National Park (actually spans bits of three provinces) -- Jirisan is the highest mountain on mainland Korea. It's beautiful... should be gorgeous in Autumn colours.
- Small towns for day trips or shorter: Gochang (big attraction: fort); Boseong (green tea fields... but nothing else, really); Damyang (an hour outside of Gwangju; attraction: bamboo forrest); Wando (beach town).
- Gwangju city's May 18 memorials (commemorating the democratisation movement & the Gwangju massacre... or "uprising", depending on who's writing the history), Mudeung Mountain
- "Lonely Korea" outdoorsy adventure tours based in Gwangju. I've never been -- I don't do "outdoorsy", but it's run by a well-travelled local guy, with a wealth of knowledge about his country & a passion for sharing it with visitors. I've heard good things about the tours.
You might want to check out Dok-do (an island that Korea & Japan both claim as theirs).
Note: I live in the south, which is why I have so few suggestions from other regions about 6 years ago
I haven't been to South Korea and it looks like amy_beloved has provided you with plenty of info. I can provide you with a bit about Thailand though...
Bangkok - It's huge and congested, but quite affordable. Hostels can be had for about $10-20 and street food, like Pad Thai, for about $3. There is plenty to see. Since the international airport is here, you'll definitely have to go through it. Worth visiting? Yes. It's also a great hub to get elsewhere in S.E. Asia.
Phuket - It's a very touristy resort town. If part of your adventures demand excessive drinking and/or prostitution, then you can find it here.
Koh Samui - Lots of really nice resorts, but hostels can be found too. More expensive than Bangkok, but it's an island. You can fly into this island.
Koh Phangan - Party island, famous for Full Moon Parties, Half-Moon Parties and Black Moon Parties. Avoid those times if you want quiet time at the beach, which are pretty nice. You can also dive Sail Rock from there, if you're into diving.
Koh Tao - During the day, go diving or snorkeling. In the evening, party or eat really well for about $15 or eat cheaply for $6. Your own bungalow can be had for $15. When I go to Thailand, I go here, because I dive.
In May of this year, 2013, I spent about $1300 for 28 days in Thailand, which covered Bangkok, Koh Samui, Koh Phangan and Koh Tao. Part of the $1300 was $430 on two weeks of unlimited diving. Subtract that way and your budget is $870. In that budget is two flights to/from Koh Samui for about $300. So, food/accommodations/transport can be had for about $570, if you exclude flying. about 6 years ago
Agree with all the previous poster says about Thailand. Keep in mind that it is the rainy season at the moment, here in Hua Hin we get some rain almost every day. In addition to the beach scene, there is plenty of interest in the North around Chaing Mai and Pai. Trekking into the countryside to visit an ethnic village is big business here. If you are interested in WW2 history, Kanchanaburi has Burma railroad and river Kwai sites to visit as well as the famous tiger temple. Transport infrastructure is very good and inexpensive. Take the buses, the trains are slow and regularly run late. about 6 years ago
In regard to Thailand, why not get off the beaten track a little? The south of Thailand is ho hum these days, although Prachuap Khiri Khan just south of Hua Hin was both a surprise and delight.
Just south of Bueng Kan in the far north east is the most remarkable temple built on seven levels of a sandstone outcrop - hard to reach but wonderful because so few do. Or in the east you might explore less known Khymer temples at Pimai or Phanom Rung. about 6 years ago