Han River is a very beautiful park where you get to rent a bicycle and go cycling around the park. Other than cycling, there is a Han River Ferry Cruise where you can hop on and enjoy the beautiful scenery.
TIP: Best to do the River Ferry Cruise at night because you get to see the amazing night scenery which appears in most of the popular Korean Drama or TV shows.
I found this information at Discoverykorea.com which is very helpful for people who want to cycling around Hangang, there are 12 bicycle rental kiosks located inside Hangang parks, and for less than $3 per hour, you can rent a bicycle built for one (or a tandem for $6). To encourage bicycle use, the city has opened another five rental facilities outside subway stations that offer free rentals for up to three hours during the week, or 2 hours on weekends. Just pre-pay and provide your I.D. or car keys as a “deposit” (see the image for details). There are also a number of other low-cost DIY rental stations popping up around the city.
Seems like there’s a lot of station where you can rent a bicycle along Han River, the one I went to is No.9 Yeouido located near Yeouinaru Station. The ferry cruise should be somewhere around that area as well.
Even if you don’t want to cycling, you can walk around the park and relax, maybe there’s a chance you bump into any Korean star or YG artist (as I know YG Building is located near to Hangang & artists always posted photo of them walking their dogs around the park).