A dear friend asked me to use my experiences to organize a little schedule for an acquaintance of her mom's that was traveling to Seoul alone. It took a lot more work than I thought it would and I thought it might be nice to post it here for other travelers to refer to if they have a week to spend in Seoul!
I've heard that you are going to visit my home for the past 5 years. I would love to be there myself to show you around but I've immigrated to Toronto instead. In lieu of that, I've written down some things you may wish to do. I've grouped the days by neighbourhood so you can do all the things there. These are just highlights. I could (and do) go on and on. I am assuming you will have access to the subway when you are there.
Day 1: Gwang-hwa-mun
This is downtown and probably a good place to get started. Get there by subway (station name is same- line 5) Palace- Gyeong-buk-gung- I think is open most days. (Museums are generally closed on Mondays.) There are two museums on either side of this palace-The newly moved Palace Museum I would recommend but I dig the whole "lost royalty" stuff. The Folk Museum was just okay. Maybe interesting for you as an introduction to Korean culture.
Lunch- if you walk out the east exit of the palace and turn north (toward the big mountain and away from the downtown) you will find a really cool street (Sam-cheong-dong street) full of cool traditional/hip places to eat. Also there is a cool place for foreigners directly across from the exit called "Seoul Selection"- it has a little cafe, Internet and tourist help. You can relax and get your bearings...
If you want, you can continue walking in that direction until you see the Blue House- this is where the president lives. My brother said it was really cool. I don't know what the situation will be when you are there. Usually certain parts are open to foreigners. Some days there are heightened alerts so they can't go in. If you can't, there is always Samcheongdong Park to the right of the turn to the Blue House. Lots of cool stuff and restaurants there which brings me to...
Dinner- you are on your own here. Perhaps you want to head back to wherever you are staying. I would personally recommend Ganga which is within walking distance directly down the street in front of the Gwanghwamun Gate (east side- down under the Seoul Finance Center Building). Pricey but the best Indian food. Yum yum yum!
Day 2: Arts and Culture
No trip to Seoul is complete without hanging out in In-sa-dong. It's my favourite haunt. To get there by subway go to Anguk station, (line 3) and follow the exit that says "Insadong!".... :) The art street is pretty amazing and I won't get into all of the stuff there but I would suggest walking down the east side, exploring and then back up the west side. Halfway down on the east side there is the bird tea house which I'm not sure how to explain to you how to get there. It's called "Old Tea House" and you can get the directions (sorta) here along with the other tea houses in Insadong. Stopping for traditional tea here is very memorable and I would recommend. For lunch there are numerous places on the side streets. They have pictures outside so be adventurous and find something new. I would recommend pa-jeon (seafood pancake) for lunch but may be too greasy for you?
After finishing the Insadong art street, you have two options. 1. On the parallel street to the west, there is the temple Jo-gye-sa. (center of Zen Buddhism in Korea-very foreigner friendly-they have a visitor's info site and offer tours although the dude's English was painful!) 2. On the perpendicular street to the northeast, there is the palace Cheong-duk-gung. This is my favourite palace of all time. You will be going at the right time to see the spring flowers and all that. You will have to hook up with a tour (no self guided until May and then it's expensive) and it's 5,000won. Check the website for times so you won't miss out. Take your camera!
Dinner- If I were you I would walk down the Insadong street again (I know, a lot of walking!) and find a place in Jongno. There are tons of yummy places. If you like cheap sushi, this is the place. At the end of the Insadong Art Street there is the small Pagoda Park ( Tapgol). It will take you like 5 minutes but the pagoda in the middle is really tall and really old and really cool. The end!
Day 3: Marketplaces
Other thing you have to do in Seoul is go to the marketplaces. I would start at the Nam-dae-mun Gate. (At Seoul Station (Line No. 1). Exit No.4, walk for 5 minutes. or at Hoeyheon Station (Line No.4) Exit No.4, walk for 5 minutes.) The park is new and you can walk under the gate now (new). Then head into the Namdaemun Market (should be visible from the gate). Wander at will and explore. You will get lost. Don't worry. There are gate numbers along the edges so keep an eye on them. This is the place to get cheap souvenirs if you are into that sort of thing. Lots of busy little places to eat. When you are done or tired or finished...ask how to get to Myeong-dong. It is across the street from the edge of Namdaemun Market. This is a fun area and if you haven't eaten there are lots of hip/cool as well as pricey places to hang out here. Lots of brandname stuff but also some cool things on the street. There are always preachers here and demonstrations. Very quirky and fun.
After this, I would get on the subway at Euljiro 1-ga Station, line 2, exit 6 (at Avatar shopping mall) and ride a couple of stops to Dongdaemun Stadium. Get off at exit No.1 and walk for 150m, then turn right to find Dong-dae-mun Market . This is more clothing stuff. Wander up around but you should eventually get to Dong-dae-mun Gate- this is the end of your day. I like that you get to see the only two remaining gates of what used to be a walled city of old Seoul. (There was a third but it was torndown like the walls. The north was protected by the mountains so no actual "gate" per se.) There are lots of places to eat in this area as well if you are looking for dinner!
Day 4: High and Low Places.
Hopefully the weather is nice today because you are going for the view- Namsan Mountain specifically. Seoul Tower/ N Tower is very well-known and can be seen from most places in the city. It's also a symbol of Seoul. The best way to get there is by Cable Car. At Exit 3 of Myeong-dong Subway Station, Line No. 4, walk toward Pacific Hotel and then walk 10 minutes to the Namsan Cable Car. (Running hours: 10:00~22:30 Fees: Above 14: Return ticket ￦7,000 / One-way ￦5,500). I would recommend walking down on your own for a different view. At the Tower there is a gift shop, bakery and coffee shop, etc. You can hang out there and see the view for free or pay to get to the very top. The park at the bottom is okay. There is a botanical garden and a sad little zoo and some monuments to some people you really don't need to know about. Plus places to lunch on the way down and at the bottom.
Next get on the subway and go to Exit #2 at Ichon Subway Station (Seoul Subway Line No. 1 and 4), walk 100m toward Yongsan Family Park. to see the National Museum of Korea. It's brand-new and holds most of the national treasures. Totally worth it.
As evening comes on, you should check out Itaewon. (Take Seoul Subway Line No.6 and get off at Itaewon Station. Come out through Exit No. 1 or No.4.) This unique neighbourhood has a great mixture of GI's, English teachers, gays, Africans and Muslims. There is a diversity of restaurants and many cool bars that feature live music. There are also dance clubs if that's your thing. Plus street vendors. The mosque is beautiful.
You might be interested in spending the night/day in a Buddhist temple. Here are the ones in the area. You will need to make reservations.
There are also guest houses in traditional beautiful hanok houses that have been lovingly restored. They are being torn down all the time so it might be a treat to stay in one. There are many- here is an affordable one in the Insadong (day # 2) area.
Yogwans- these are hotels but not geared toward westerners. Cheaper and I think totally comfortable. Some are "love motels" but most aren't. The "love motels" btw don't offer companionship. It's just a place to stay. You have to come up with the company on your own. :)
(Note that everything I've planned for you is on the northside of the river. Only a small portion of the city but this would be old Seoul more or less.)
Other things to do if time/interest permits:
*Han River Ferry Cruise - cheap and fun. Also night is beautiful.
*Cheong-gye-Cheon (stream)- an easy flat walk that you can do for as long or little as you like or have time for. Goes through the middle of the city and has cool art and sights. I would recommend doing the whole bit starting at Gwanghwamun (Day 1) and ending up at Seoul Forest. Rent a bike here and cruise around the forest because it's plenty big!
*Seonyudo- island park- My favourite park hands down. It's totally cool renovated water treatment plant. On Sundays there usually are Korean middle schoolers who dress up in outrageous Japanese Animae characters. Nice little cafe there that also serves so-so chicken and other snacks.
Good luck! Please let me know if there is further information you wanted.