Free history at Sejong University Museum, Seoul, Korea
To get to the university and the museum, go to Children's Grand Park Station on Line 7, and take exit 6. The university is right at this exit; you should be able to see the large, traditional building just inside the campus. Walk through the old traditional gate to get inside the campus. The campus has some restaurants/cafes where you can take a break, including a nice coffee shop in the new building next to the old gate.
Across the street is Children's Grand Park, which has a lot to see and do as well, though I haven't visited it yet as I've been waiting for the amusement park inside to reopen after extensive renovations.