Gyeongbokgung Palace is an extremely popular place to visit in Seoul. In the summer it can get really hot if you want to dress in traditional hanbok. My suggestion would be to visit the National Palace Museum of Korea right next to the palace. The museum has three floors full of history and it free as well. It is perfect to cool off in the summer but also really educational and I would recommend visiting whenever you travel to Seoul.
The museum covers around 500 years of history starting from the Joseon Dynasty. The Museum starts on the second floor and has different sections covering the Kings of the Joseon Dynasty, Joseon Palaces, Royal Court life, and a Special Exhibition Gallery. The first floor has sections covering the Korea Empire, Royal Vehicles and two mor4e Special Exhibition Galleries. The bottom floor covers Painting and Calligraphy, Royal Rituals, Scientific Acheivements, a visable storage section, and an education space.
The museum is very large and you could easily spend over two hours exploring and learning about history. One of my favorite parts of the museum was the scale model of Gyeongbokgung palace before and after Japanese occupation. Another thing I really enjoyed learning about was the jagyeongnu, a self-striking water clock. The museum hosts a restoration and it is really cool to see it when the gong is struck. There is also a video shown on the wall of how the flow of water makes it work.
I think if you are interested in Korean history, this museum is a great place to visit!