Seoul is one part high-tech city one part peaceful temples and palaces. I'm overgeneralizing but there's definitely a very breathtaking contrast between the feeling you get running around town versus when you step foot in its various palace or temple grounds. It's like instant peace.
If you're wondering where to travel within South Korea, specifically Seoul, I would suggest making sure to visit one of its top travel sites, Gyeongbokgung Palace (above). It's the oldest of Five Grand Palaces built during the Joseon Dynasty (1392-1910) and its name means, "the greatly blessed palace." The Bugaksan Mountain stands watch behind it and Haechi (mythical lion-like creatures) stand in front of the palace main gate, Gwanghwamun Gate, to ward off danger. As you can see in the photo above, it's popular to dress in a traditional hanbok to visit.
In fact, Seoul's five palaces, Gyeongbokgung, Changdeokgung, Changgyeonggung, Deoksugung, and Gyeonghuigung all waive admission fees for visitors wearing hanbok.
Hanboks can be rented for around $13 at places like Eulji-ro Underground Shopping Center. We saw a lot of young Koreans dressing from head to toe in traditional Korean clothing around the palace. Nowadays it's a very popular thing for young folks there to do, for Instagram.
We didn't see too many foreigners doing it though, and we stopped by Gyeongbokgung Palace on our way back from a news shoot so we arrived unprepared. But I would highly suggest taking part when you visit, it's definitely encouraged so there's no worry of appropriation. Rather it's a way to take part in the culture when you visit and really get a feeling for the historical dress.