Busan is where Lane’s cousins live, and where she will be spending the summer from June to August 2001. The city was called Pusan until 2000, and is pronounced like Pusan (at least that’s how it sounds to English-speakers).
Busan is the second-biggest city in South Korea, and has a population of over 3 million. It is the economic centre of south-eastern Korea, and has a large industrial area, and the biggest port in Korea. It is called the summer capital of Korea, since it has a number of beaches to attract tourists, along with cafes, restaurants, and shopping districts to cater to them.
It is unknown whether Mr and Mrs Kim, or their families, are originally from the Busan area as well as the cousins, but it doesn’t seem too unlikely.