On Liberation Day (광복절-光復節) August 15, 2010, the newly reconstructed Gwanghwamun was open to the public. As long as I can remember, Gwanghwamun has been covered due to the construction, and I guess has been since 2006.
The history of Gwanghwamun is quite an interesting one. There's a good Wikipedia article here, but basically it was built in the Joseon Dynasty in 1395, then it was destroyed durring the Imjin war with Japan in 1592. It was reconstructed in 1867, but was torn down and relocated slightly during the Japanese occupation to make way for the Japanese Governor General Building. Then it was destroyed again during the Korean war and rebuilt with concrete in 1963. Finally in 2006 they decided to restore it to it's original position and original grandeur which is now finally viewable. (Please don't quote me here because the more sources I read, I keep getting slightly different dates and facts... this seems to be the closest to the truth I can get)
The location of the gate is very important because it must line up correctly with the rest of Gyeongbukgung palace behind it, but even more importantly, it must be in the correct fung shui (pungsu in Korea), or correct alignment with the mountain behind and the river in front. When the Japanese relocated the structure, it was no longer in the proper alignment with not only the palace, but with it's natural surroundings. (See here for another article)
Sejeongno, which runs north past the Cheonggyechong up to Gwanghwamun is a very historic street as well. Last summer a plaza was opened, running down the center of the street. Here you can find the famous monument to General Lee Sunshin, but that's just the begining.
Here is the statue of Lee Sunshin. As you can see, there are fountains on all sides, which I like to think of as Lee Sunshin's water park. Kids have a ball playing in the water here all summer long. It's like going to Oceanworld, I suspect, but without the lines and the prices.
If you keep walking past the wet children you'll come across a giant statue of King Sejeong, the most famous of the Korean kings and the inventor of Hangul amoung many other things.
Go around to the back side and you'll find an entire museum dedicated to King Sejong the Great and General Lee Sunshin below. The admission is free, so there's no reason no to check it out while you're in the area.
There was also a performance of traditional musical instruments here when I visited. First each played some more traditional music, but then got together and played some more modern songs with their instruments.
After leaving here I stumbled upon yet another museum. This was called Green Growth Korea and it was just a small museum dedicated to ideas for a greener future. It was also free, so I went in to check it out.
Here is Korea's energy usage for the past number of years. The last column is a projection for the year 2030.
Here is a model city with lots of little ideas for energy production and conservation. One cool one I liked was "solar trees" which were poles with solar panels on the top. I think solar panels are going to have to get a bit more efficient in order for that one to work out though...
When you get a chance, be sure to check out the new Gwanghwamun, Gyeongbukgung Palace and everything around Gwanghwamun Plaza. Everything except palace has free admission, so it can make for a cheap weekend afternoon. Take line 5 to Gwanghwamun Station or Line 1 or 2 to City Hall and walk 5 minutes.