It's bad enough driving in Seoul, but riding a bike on regular city streets is not just unpleasant, it's virtually suicidal. However, there are some good biking trails along the Han-gahng and in Olympic Park. The most popular trail along the river spans 37km (23 miles) from Yanghwa to Gwangnaru. It takes about 2 1/2 to 3 hours to reach Yangcheon from Gwangnaru.
Bikes can be rented cheaply throughout the city (usually for about W3,000 for an hour, W6,000 for tandems). Rental bikes are usually well used and old, but sturdy. The most convenient rental places are at Ichon Station (subway lines 1 or 4, exit 4) toward the Turtle Boat and Yeouinaru Station (line 5, exit 2) toward the underpass to Yeouido Park. Both Ichon and Yeouido parks can get pretty crowded on weekends, so Olympic Park might be a better bet.
Golfing is a popular sport in South Korea and there's no shortage of courses. There are only two within the city of Seoul, but 46 in Gyeonggi-do alone. However, the prices aren't reasonable to most visitors, and even prohibitive for most natives (costing over W200,000 for 18 holes and a caddy). Golf is seen as a sport for the upper crust, and that's why most Koreans travel to other countries for their golf vacations. A better option for practicing your swing is to try one of the many indoor driving ranges in the city. Almost all luxury hotels in the city offer a driving range and most of them cost W10,000 to W20,000 per hour.
There is no shortage of hiking opportunities around Seoul. The slopes around the city offer relatively easy climbs. The hills and mountains in the vicinity get especially crowded during the pretty seasons of spring and fall. There are 37 mountains in the vicinity of Seoul with Bukhansan (Mt. Bukhan) being the highest (837m/2,746 ft.) and drawing most of the crowds.
A good option is the centrally located Namsan Park, which has a variety of trails. Take subway line 4 to Chungmuro Station (exit 2) or line 3 to Dongguk University Station (exit 6) and take the Namsan loop bus after you exit the subway. Get off at the National Theatre, walk straight, and turn right. The trail starts on the left side of the traffic control booth.
Another easy hike is Achasan (Mt. Acha), which is not too steep but offers a good view of the Han River. It takes only about an hour to climb up to the top and back, but you can lengthen the hike to over 2 hours by climbing up Achasan over to Yongmasan and back. Take subway line 5 to Achasan Station (exit 2) and turn left at the first intersection. Keep walking until you get to the T-section and turn right. Walk for about 200m (656 ft.) more, past the temple, Hwayangsa, and you'll see the entrance to Daeseong-am, which leads to Achasan.
Nearby Yongmasan (Mt. Yongma) is an excellent hike with a variety of views and some fun things to see along the way, like a man-made waterfall and the remains of a small fort dating back to the Goguryeon period. Some parts of the trail can get a bit steep, so it's best to wear hiking boots. Take subway line 7 to Yongmasan Station (exit 2) and walk through the entrance to the Hanshin apartments. Go up the stairs next to the pavilion, past the playground and turn right. Next to the exercise facility, behind the wire fence, there are stairs that lead you up to the trails.
The most popular hike in the Gangman area is on Umyeonsan (Mt. Umyeon). It will take you about an hour to hike to the mountain's main temple, Daesongsa. Plan to spend some time at the Seoul Arts Center when you reach the bottom. Take subway line 3 to the Nambu Express Bus Terminal (exit 5). Walk straight and turn right at the first intersection to the Seoul Arts Center (about a 10-min. walk). Take the overpass in front of the arts center which leads to the hiking trail.