We live South of the river, but just a short 5 minute walk from the Han River. There is a nice riverside park that runs the length of the river (I think someone told me it runs about 20 miles or so). There is a bike and running path (complete with green astro-turf...good for the knees), and along the way they have exercise machines spaced out along the path.
You can see one of the bridges in my picture that connects Northern and Southern Seoul. I think Kay (our driver) told us there were 22 or 27 bridges along the river. We live near the Dongjak Bridge.