I was having second thoughts on whether to book for DMZ tour or not as it is expensive. In the end, we book the half-day DMZ Tour which costs 38000 KRW / pax and the itinerary is as follows: 

Hotel pick up -> Imjingak Park -> The Bridge of Freedom -> The 3rd Infiltration Tunnel -> DMZ Theater/Exhibition Hall -> Dora Observatory -> Dorasan Station -> Unification Village (pass by) -> Amethyst/Ginseng Center -> Arrive at City Hall/Itaewon

It wasn't complete though as we didn't go for the JSA.  They say the JSA is the divide between North and South Korea where they stand like statues and stare at each other..hehe... and being with them will give anyone "the chills".  Nevertheless, it was a valuable experience for a person residing in a peaceful country. It is a great reminder of the status of South Korea with its relation to its neighbour to the North. I was amazed to learn about how far the North Koreans had come in their attempts to create infiltration tunnels into the South. The tour is something that every visitor to Korea should experience to further understand the reality of the relationship between North and South Korea and the desire of the people to see the Nation reunited one day.

Cheonggyecheon stream (청계천) is located in downtown Seoul. The stream has a path on both sides and decorated with art, statues or special themes for events. At night-time parts of the river light up and you can enjoy a laser show. It is recommended to start at the stream near Gwanghwamun station where special events and concerts are held. There was lantern display at the time of our visit.

Here is cost breakdown.

The room at Seoul Hostel Center is very small. It doesn't have heater or aircon. If you are not fuzzy and would just book a place to sleep, then you may consider this hostel. It is walking distance to a lot of tourist attractions like Gyeongbokgung palace, Gwanghamun Plaza, Insadong, Cheonggyecheon Stream, Myeongdong, Namdaemun market and a lot more...

After we checked-in at the hostel, we walked back to Jonggak Station. The order of our Seoul City Tour is as follows:

Bosingak Bell Pavilion (보신각) houses the Bosingak. Bosingak is a large bell pavilion on Jongno in Seoul, South Korea. The bell in Bosingak gives Jongno its name, which literally means "bell street." It was originally constructed in 1396 but destroyed many times by both war and fire. It was designated Bosingak by Emperor Gojong in 1895. Under the Joseon Dynasty the bell was rung to announce the time, several times a day and to signal the opening and closing of the city gates as well it was used as a fire alarm. In modern times, the bell is rung only at midnight on New Year's Eve. Because of the massive number of people who attend this ceremony, Metro trains on Line 1 of the Seoul Subway do not stop at Jonggak Station on New Year's Eve. Source: wikipedia. It is at Jonggak Station exit 4, across Jongno Tower (종로 타워)

Jogyesa Temple (조계사) does not give off the solemn and traditional air of the other temples located deep in the mountains, or offer the seasonal scenery of the mountains and the sea, since it is located in the middle of the city. It is easily accessible from Jonggak Station Exit 2, from there walk towards cafe7gram and cross the street towards Dunkin Donuts, walk a little further until you reach this temple.

Ujeongchongguk or "Postal Administration Office of Joseon" is less than hundred meters away from Jogyesa Temple. This might not be known to tourists, we happened to discover it while walking. It is the first post office founded in 1884 in Korea and now serves as a memorial building for post. You can find stamps and documentary records preserved in this building. 

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Gwanghamun Gate (광화문) is the main gate of Gyeongbokgung Palace. Literally it means “may the light of enlightenment blanket the world”, and implies the resounding dedication the people of the Joseon Dynasty had in creating a new dynasty.

Gyeongbokgung Palace (경복궁) is a royal palace located in northern Seoul. It was the main and largest palace of the Five Grand Palaces built by the Joseon Dynasty. The name means "Palace" [Gung] "Greatly Blessed by Heaven" [Gyeongbok]. Admission to this palace allows you to also visit National Palace Museum of Korea (국립고궁박물관) and National Folk Museum of Korea (국립민속박물관).
Gwanghamun Plaza (광화문광장) is a plaza  in front of Gwanghamun Gate. Aside being famous to "City Hunter" drama fans, this place tells more a historical story. Be sure to learn more about King Sejong the Great who developed Hangeul and Admiral Yi Sun-Shin who is a Korean Naval Commander.

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From Gwanghamun Plaza, walk towards City Hall and turn left in between Kyobo Bldg and Gwanghamun Post Office, you will soon see Jongno Tower again. You can take train from Jonggak station to go to Chungmuro Station OR if you still feel like exploring the place, walk toward Bosingak and continue to walk straight until you reach Jongno-3 station. From Chungmuro Station, take yellow bus#2 or bus#5 to Namsan Park.

N Seoul Tower (N 서울타워) is commonly known as the Namsan Tower or Seoul Tower, is a communication and observation tower located on Mt. Namsan and is the highest in Seoul and offers a stunning view of the city. Catch the beautiful light show every 8:30 PM

Here is cost breakdown.

I'm a frugal adventurous traveller thus going on travel with me means taking public transportation, a lot of exploration by foot and constant interaction with local residence. This I would warn my co-travellers before going on a trip, besides group tours doesn't give you the full travel experience.

The transportation system in Korea is easy, convenient and most of all cheap. But you must plan your route carefully as you should consider travel timing and distance between sites to visit. However, language could be barrier as few Koreans could speak English. A basic Hangeul lessons and body language would be helpful. Although you might not probably remember your Hangeul lessons, you can try to interpret what they are saying...hehe :p You can visit Talk To Me In Korean for some lessons, it really helped me a lot :) Also, write down the places in Korean in case you might need help with directions. Koreans are very friendly and helpful people, they will go to the extent of bringing you to the place you are looking for.

Total Expenses:

Item	Cost (SGD)
Plane from Singapore to Cebu  (return)	105
Plane from Cebu to Incheon (return)	80
Plane from Gimpo to Jeju Island (return)	68
2 Nights at Feliz Telcon Hostel	45
1 night at HK Jeju Hostel	17
3 Nights at Seoul Hostel Center	45
Total Daily Expenses	260
Souvenir and Shopping	65
Total	685 per pax

Daily Expenses Breakdown:

Item	Cost (KRW)
Day 1	31850
Day 2	33300
Day 3	20890
Day 4	12550
Day 5	43000
Day 6	47100
Day 7	41450
Total	230140