Here's an ideal itinerary for 3 days in Korea:

Day 1:

• Start your day with a visit to Gyeongbokgung Palace, the largest and most iconic palace in Seoul. You can watch the changing of the guard ceremony and explore the palace grounds.
• After the palace, head to Insadong, a charming neighborhood filled with traditional Korean crafts, tea shops, and street food. You can also visit the Ssamziegil shopping complex, which has unique boutiques and galleries.
• For lunch, try some Korean barbecue at a local restaurant. It's a must-try dish in Korea!
• In the afternoon, visit Namsan Tower, a popular tourist spot with stunning views of the city. You can take a cable car up to the tower and enjoy the panoramic views.
• End your day with a visit to Myeong-dong, a bustling shopping district with street food, cosmetics, and fashion. You can also try some Korean fried chicken for dinner.

Day 2:

• Start your day with a visit to Bukchon Hanok Village, a traditional Korean village with beautiful hanok houses. You can also visit the Bukchon Cultural Center to learn more about Korean culture.
• After Bukchon, head to Changdeokgung Palace, another beautiful palace with a stunning garden. You can take a guided tour to learn more about the history of the palace.
• For lunch, try some bibimbap, a popular Korean dish with rice, vegetables, and meat. You can find it at many local restaurants.
• In the afternoon, visit the National Museum of Korea, which has a vast collection of Korean art and artifacts. You can also visit the nearby War Memorial of Korea to learn more about Korean history.
• End your day with a visit to Hongdae, a trendy neighborhood with street performers, cafes, and nightlife. You can try some Korean craft beer and listen to live music.

Day 3:

• Start your day with a visit to the DMZ, the demilitarized zone between North and South Korea. You can take a guided tour to learn more about the history of the Korean War and see the border between the two countries.
• After the DMZ, head to Itaewon, a multicultural neighborhood with international cuisine and shopping. You can try some Middle Eastern food or visit the antique market.
• For lunch, try some Korean street food at Gwangjang Market, a bustling market with a variety of food stalls.
• In the afternoon, visit the Seoul Museum of Art, which has a collection of contemporary Korean art. You can also visit the nearby Cheonggyecheon Stream, a beautiful urban park.
• End your day with a visit to Gangnam, a trendy neighborhood with high-end shopping and nightlife. You can try some Korean fusion cuisine and visit a rooftop bar for a view of the city.