To my mind, the best thing about this museum is the large scale model of the city (or most of it, anyway), part of which is covered by glass floor. In the last pic above, you can see the World Cup Stadium, and in the pic below, my apartment building is A, the school is B (click to see a larger version). Pretty cool.
There are several smaller "mock-ups" including a classic mixed use building--stores below, apartments above.
There are also full scale transplants including a typical tiny restaurant and a flat from the mid-eighties. "Steve the Butler" on the top shelf there, not a toy I remember in America. And I would.
Lots of other cultural effluvia like this lovely fashion poster.
The exterior space is pretty well used, including some architectural education, a minibus from the 1988 Olympics and old Seoul tram car.
A display about the way Seoul grew and grew after the end of the Korean War included this interesting panel:
The Seoul Museum of History is located midway between Seodaemun and Gwanghwamun stations on the 5 line. It's free. If you have a QR scanner, you can read a fair amount of English info about the exhibits.