The Bundang Subway Line stops in all the major areas of Bundang, and is very convient.
Many buses run between all the different areas of Bundang. Buses are the best way to get back and forth between Bundang and Seoul, even during rush hour (8pm) a bus can get from Bundang to Insadong in 40 minutes. This trip will cost about 1,700 wan. You can also catch a airport limousines to Incheon and Kimpo internation airport from major Bundang subway stations. The price is about 12,000 wan each way.
Taxis can be used, but they are not as ubiquitous as in Seoul. During commute times it is near impossible to find a free taxi. At night, however, there should be no problem. Ask about your destination before you get in, as some taxis will only take you to certain areas (for example, some taxis are only for trips to Seoul, and cannot take you around Bundang) Most local taxis will not run the meter to Seoul and will ask for 30-40k wan for the trip.
Central Park, near Seohyeon Station and Sunae Station, is a beautiful place to stroll around. You can see an old Korean house as well, the last remaining house from the traditional village that existed in Bundang during the Joseon era.
Tancheon, the small river that runs through Bundang, has excellent walking and cycling paths along both banks. Additionally, there are basketball courts and grassy fields up and down the river, as well as a small golf course near Sunae station.
A wide variety of drinking establishments can be found around every subway station. Seohyeon and Jeongja stations are good places to start, with the majority of "Western Bars" being at Seohyeon station in the shopping corridors directly outside of AK Plaza(Samsung Plaza)'s two main entrances. Popular western bars in this location include: Amuse, Monkey Beach, Dublin, Lose Control, and Traveler's Bar & Grill.