This is an easy side trip for the whole family.
Eongtto Falls (엉또폭포) is a 50 meter waterfall that plunges off a cliff into a cool pond. However, make sure it's the rainy season or has rained at least one centimeter recently, or else you'll only be greeted by a 50 meter dry cliff!
Parking is available alongside the very narrow road you'll have to take to get there, with room for perhaps 20 cars. Hike to the west end of the parking spaces and follow the sidewalk along the road over the river. The sidewalk is actually nice and looks like inlaid stones. You'll see what looks like a road on your right that heads east along the side of the river. Follow that, and it will soon become the path.
The actual trail is very well made and mostly passes through forest. An open section with nice views of the cliffs crosses a boardwalk. Right after that, you'll come to a nice observation platform that offers great views of the falls. Take your time enjoying the falls and then retrace your steps back.
Eongtto (say Oong - Doh with a soft "o" and very strong/sharp "D") Falls can be spectacular, or disappointing. Regardless, the hike there is fairly nice and the scenery good, so it won't be a total waste of time if it's not flowing! It is also a lot less crowded than other areas in Jeju, which can be nice if you're looking for a bit of solitude.