Expenses
Everything's in Korean Won (KRW) with a conversion rate of PHP 1 to KRW 25.24.
4650 - Train to Hongik University from airport
23950 - Transportation expenses
86300 - Food and drinks
27700 - 2 nights at Hostel Maru
2500 - Miscellaneous
500 - Use of telescope at DMZ observatory
1000 - Ticket to enter Dorasan Station at DMZ
3000 - T-Money Card
10000 - Combination ticket for palaces and temples
16000 - Postcards
1000 - Suwon Fortress ticket
1500 - Hwaseong Haenggung Palace ticket
178100 - Total
*I managed to spend less on accommodation because I found someone to host me for 2 nights, which significantly reduced my expenses. If you go shopping, you will definitely spend more, so plan accordingly.
Itinerary
For 5 days I wasn't able to cover some places I wanted to go to, because it rained a few times during my trip. Not visiting all the places I wanted to see gives me reason to return.
Day 1
Arrival
Check-in Hostel Maru
Explore Hongdae and nearby areas
Day 2
DMZ Tour
War Memorial of Korea
Day 3
Jongmyo
Gyeongbokgung Palace
Changdeokgung Palace
Changgyeonggung Palace
Explore Myeongdong
Day 4
Explore Suwon Fortress
Hwaseong Haenggung Palace
Day 5
Depart for Manila
I could've gone to more places, but there were times when I was too tired to travel longer and it rained a couple of times during my trip. You could visit more places depending on your pace and itinerary.
The DMZ and War Memorial of Korea are noteworthy destinations for those interested in history. The Suwon Fortress is far but worth the trip if you are interested in a not so visited attraction, it is also a UNESCO Heritage Site. You don't have to visit a lot of the palaces since they mostly look the same anyway, a stop at Gyeongbokgung and Changdeokgung are enough will buy you more time to visit other places. Myeongdong and Hongdae are shopping and dining areas for those who want to go on a food trip or shop till they drop.
Seoul and its nearby areas preserved their cultural and historical heritage, making the city distinctly Korean despite its commercialization and modernization. It has an old and new soul that gives it personality.
Here's a link to my other posts about Korea:
http://www.thewanderingjuan.net/search/label/Korea