Traveling to China you are going to have to deal with crowds. From my experience the best time to go is at sunset at the Mutianyu location where you can take a ski lift up and hike the wall and ride a luge down the mountain! It was the absolute best experience! I was able to get amazing photo's without a crowd of people and be able to experience what it must have been like as a Chinese soldier watching for the Mongolians. Truly the best way to experience the Great wall of China! It is a little farther outside the city than the normal locations but booking tours (typically in China you book with external tour guides who show up with a van and tour you around, most of the time you'll need to make sure you've eaten because they don't stop on the way to feed you) will take you right to it and it is soooooo worth it to not have to search through crowds!
Culture and experiences
Mutianyu is the best location for the Great Wall, souvenirs, transportation up and down, and go at sunset to get low crowds!!