Located near "downtown" Seoul*, the Agricultural Museum has an extensive look at Korea's heritage and future on the farms.
The museum is open 9:30-18:00 (17:30 November through February), closed Mondays. Admission is free. Take the subway Line 5 to Seodaemun Station; it's about a three minute walk from there along the main road. Just look for the gold sign at the top of the building as you can see in one of the photos at the top of this post.