Beijing can be overwhelming at times but a great time to visit is during winter. The pollution is not terrible since the air is cold and dry and there are very few people out and about. Of course, this means that you will have to brave the cold but it’s no worse that New York in the winter and you will get the whole place to yourself.
You can hit all of the hot spots (the Forbidden Palace, the Summer Palace, and the Great Wall) and see virtually no people.
For visiting the Great Wall, I like to visit it at Mutianyu, which is about 70 km outside of Beijing. The wall is in great shape here and you can walk for ages and ages with very few people around.
Also, the cold makes it that much nicer when you rush into a warm restaurant for a hot meal. My favorites for food in Beijing are Haidilao for hot pot (a big steaming broth is brought to your table and you cook your meat,seafood, and fresh vegetables by dunking them into it), Dadong for peking duck, and NaJia XiaoGuan (Haidian, Wofo Temple West Road) for Manchurian food (royal soup with all kinds of eastern medicine that’s supposed to be good for you, egglant, pork belly, and Chinese yam with flower sauce).