The Great Wall?

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Your plan sounds feasible, and visiting both Mutianyu and Simatai will offer very different experiences. On a clear day, Mutianyu provides a 360 degree view of the surrounding mountains, while Simatai is famous for its illuminated night scenery. Gubei Water Town is also beautifully lit up in the evening, adding to the charm of the experience.

Late November can be a bit cold, but most hotels in Gubei Water Town offer convenient packages that include accommodation, admission, hot spring access, and Great Wall tickets, making it a comfortable and worthwhile stay. If you need any photos for reference, I’d be happy to share some with you. Also, your itinerary is absolutely doable within a day.

For the remaining three nights in Beijing, you can consider activities that kids would enjoy, such as visiting local residences, dumpling-making, traditional paper cutting, Peking Opera, or acrobatics performances. These can add a cultural and hands-on element to your trip.

Let me know if you need any recommendations or further assistance.