Seoul has so many palaces that are worth visiting it is hard to know which ones to see and which ones to skip if you have limited time. I only had a chance to see 4 of the 5 Grand Palaces in Seoul. Below are the top ones I think are worth seeing, in order of most beautiful to least (although lets be real the least beautiful one is still pretty dang beautiful).
Little bit of history....Urban and civil planning was a key concept when Seoul was first designed to serve as capital in the 14th century. The Joseon Dynasty built the Five Grand Palaces in Seoul and they are all located relatively close to each other. (Source: Wikipedia)
Changdeokgung was the most favored palace of the Joseon princes and it blends with the natural topography of the site instead of imposing itself upon it. (Source: Wikipedia)
Absolutely beautiful layout of palaces but the secret garden in the back is where you will spend most of your time. It costs more but it is completely worth it. You have to buy tickets for a specific time to enter but once you are inside you can spend as much time wandering as you want. Secret garden pictured above.
The oldest and grandest of the Seoul palaces, a little stark and dry but the pavilion in the back of the complex is a stunner. (pictured above)
Located right next to Changdeokgung and easily accessible if only for 5 minutes but definitely the least impressive of the 4.
Each palace costs a bit different but buy the Palace saver pass at any of them for entrance to all of the palaces and the royal shrine. It costs 10,000 won (about $9 when I was there) and is completely worth it. Especially if you are visiting the secret garden in Changdeokgung which bought alone costs 8,000 won. Below is a great map of how close some of the sites are that are included in the Palace saver pass. (Full credit for map goes to Skipping Clouds - She also has a great write up on visiting the Palaces)