Here's a fun and family-friendly itinerary for 10 days in Seoul:

Day 1: Arrival in Seoul

• Check into your accommodation and relax after your journey.
• Take a leisurely stroll around your neighborhood to get a feel for the city.
• Enjoy a traditional Korean dinner at a local restaurant.

Day 2: Explore Insadong and Bukchon Hanok Village

• Start your day with a visit to Insadong, known for its traditional Korean culture and arts.
• Wander through the charming streets lined with shops selling crafts, antiques, and souvenirs.
• Head to Bukchon Hanok Village to see well-preserved traditional Korean houses.
• Visit a Hanbok rental shop and dress up in traditional Korean attire for a fun family photo session.

Day 3: Gyeongbokgung Palace and National Folk Museum

• Spend the morning exploring Gyeongbokgung Palace, the largest of the Five Grand Palaces built during the Joseon Dynasty.
• Visit the National Folk Museum located within the palace grounds to learn about Korean history and culture.
• Enjoy a picnic lunch in the palace gardens or nearby Gwanghwamun Square.

Day 4: Lotte World and Lotte World Tower

• Head to Lotte World, a massive indoor theme park with rides, shows, and an ice rink.
• After a day of fun at Lotte World, take a short walk to Lotte World Tower, one of the tallest buildings in the world.
• Visit the observation deck for panoramic views of Seoul and enjoy dinner at one of the tower's restaurants.

Day 5: Namsan Seoul Tower and Myeongdong Shopping

• Start your day with a visit to Namsan Seoul Tower for breathtaking views of the city.
• Explore the surrounding Namsan Park and take a family photo with the iconic "love locks."
• Head to Myeongdong for some shopping and street food tasting. Don't miss trying Korean skincare products and cosmetics.

Day 6: DMZ Tour

• Take a day trip to the Demilitarized Zone (DMZ) to learn about the history of the Korean War and the division between North and South Korea.
• Visit the Third Infiltration Tunnel, Dora Observatory, and Dorasan Station.
• Return to Seoul in the evening and unwind with a relaxing dinner.

Day 7: Hangang River Cruise and Han River Park

• Enjoy a leisurely cruise along the Hangang River, taking in the scenic views of Seoul's skyline.
• After the cruise, explore one of the Han River Parks for a relaxing afternoon picnic or bike ride.
• Consider renting a family-sized bike or a paddleboat for some outdoor fun.

Day 8: Korean Cooking Class and Insadong Street Food Tour

• Take a family-friendly Korean cooking class to learn how to make traditional dishes like bibimbap or bulgogi.
• After the class, explore Insadong for a street food tour, trying various Korean snacks and desserts.
• Don't miss the opportunity to taste hotteok (sweet pancakes) and tteokbokki (spicy rice cakes).

Day 9: Everland Theme Park

• Spend the day at Everland, South Korea's largest theme park, located just outside of Seoul.
• Enjoy thrilling rides, animal encounters at the zoo, and colorful parades.
• Wrap up the day with a fireworks show before heading back to Seoul.

Day 10: Departure

• Depending on your flight time, you can squeeze in some last-minute shopping or visit a local market for souvenirs.
• Check out of your accommodation and head to the airport for your departure.

I hope this itinerary gives you a good mix of cultural experiences, family-friendly activities, and fun adventures during your 10 days in Seoul! Let me know if you need any more suggestions or tips. Safe travels!