There are several answers to this question: the best time of the year, the best time of the month, best time of the week, and the best time of the day. Here, I will comment on them separately.
The best time of the year is the most important decision as this will affect the climate and the appearance of the Great Wall and its surroundings. Summer provides beautiful green foliage; fall provides beautiful autumn colors and red maples, winter brings snow which presents the Great Wall in a whole new spectacular way, while spring makes the Great Wall full of vigor.
In general, it is more comfortable to visit when the weather is mild. Beijing has hot summers and cold winters, so spring and fall are the best time of the year.
* Dust storms can occur during March and April.
* Chinese New Year festival generally lasts about 15 days, and many businesses close during this period and public transportation is very crowded.
Try to time your visit to the Great Wall to coincide with the full moon. This will provide more light when the sunlight fades, and may give you some opportunities for good photographs, and make your trip more memorable.
Note: The full moon dates are the same worldwide.
Try to visit the Great Wall during the week rather than on the weekend, especially if going to the main tourist locations. Traffic on the roads and crowding on the Great Wall will be significantly reduced.
Afternoon is warmest and best in winter; afternoon is hottest and worst time in summer; all day is comfortable in spring and fall. Sunrise and sunset are the best times for photography.