Although Insadong has become a bit of a tourist trap, I still enjoy going there because you never know what you'll encounter or discover. Art exhibits showcase local talent, performances enrich understanding of cultural traditions, protests give insight into current affairs, and shops show artisans at work on their crafts. It's a fun, inspiring place to spend an afternoon. And if you are visiting Seoul for the first time, then you absolutely have to put Insadong on your list. For a broader description of what to do in Insadong, check out this post from Culture Trip, which provides an excellent list of "to do's" (wear a hanbok, eat street food, insert yourself into "live art"...).
You can easily walk to Insadong from Anguk Station, which reminds me: when you travel to Seoul, definitely download the Subway app for your phone (app icon shown here). It's super simple to use. You click on your departure station and your arrival station and the app will show you how to navigate through the metro system. You can choose the fastest, shortest, or path with least connections.