Busan
http://english.visitkorea.or.kr/enu/SI/SI_EN_3_1_1_1.jsp?areaCode=6
Busan has some nice places to visit that are accessible from the subway. City bus tour also makes it easy to see local points of interest.
http://www.citytourbusan.com/cityworld/eng/01_info/info_01.jsp
Places to visit: PIFF Square, Taejeonngdae Resort Park, Jagalchi Market, and Busan Aquarium.
http://www.citytourbusan.com/cityworld/eng/01_info/info_01.jsp
Gyeongju
http://english.visitkorea.or.kr/enu/SI/SI_EN_3_1_1_1.jsp?areaCode=35,2
Here’s a nice daytrip for Gyeongju.
Cheonmachong Tomb( Tumuli Park ) - rediscovered ancient burial mounds where past royalty are buried.. Get an early start and begin your trip here.
Cheomseongdae Observatory - also located here. Continue on to the Gyeongju National Museum.
Gyeongju National Museum - exhibit of artifacts from the tombs. Learn about this important part of Korea’s history. Across the street you can take a short walk around Anapji Pond. From the museum, continue on to Bulgeoksa. Time for a break. Have lunch across the street at one of the many tourist restaurants.
Bulguksa Temple - most famous Buddhist temple in Korea. Several buildings to walk around. Working monastery. Continue on to Seokguram Grotto.
Seokguram Grotto(Mt. Tohamsan) - short hike to view a statue of Buddha housed in a cave on a mountain top. End trip here, returning to town for dinner.
Edited by: thehelpfultraveler