Gyeonggi-do (Gyeonggi province) is like a giant doughnut surrounding the city of Seoul. In fact, Seoul gave this province its name, back in 1018, during the Goryeo Dynasty. "Gyeong" means "capital city designated by the king" and "gi" means "150 kilometers of land in the four directions from where the king lived." How's that for a mouthful?
Located in the northwestern part of South Korea, the fertile plains created by the Han River have made Gyeonggi-do ideal farmland, and it's been inhabited since prehistoric times. Today, it is the most populous of South Korea's provinces and includes the cities of Incheon (home to the airport where you most likely arrived), Suwon (the provincial capital), and Icheon (the ceramics center of the country).
The province is now largely industrial, thanks to overflow from Seoul -- indeed, it's sometimes difficult to tell where Seoul ends and the province begins. Still, you can see traces of South Korea's not-so-distant agricultural past in the rice paddies and fields that remain. It is an eclectic province encompassing high-tech developments, remnants of Korea's agrarian history, and traces of traditional art and culture.
Gyeonggi-do borders the Yellow Sea, and Pyongtaek Harbor, the closest harbor to China. More interestingly, Gyeonggi-do also borders North Korea's Hwanghae province. In fact, the top part of Gyeonggi-do was lopped off when the country was split in two.
All areas of the province can be enjoyed as day trips from Seoul. However, if you're planning on spending more than a day here, you may want to overnight in one of the province's cities. Buses are the fastest and least expensive way to get around, but Seoul's subway system extends to parts of the province. Regular and express trains are also available.