Beijing is on behalf of the North, Shanghai is on behalf of the eastern coast, Shenzhen is on behalf of the Chinese forefront economy; Chongqing and Chengdu are on behalf of the Midwest. The pace/ rhythm of people’ lives in the east and southeast is much faster than that in the west. It depends on what kind of life you prefer. Beijing is famous for its magnificent and grand/ imperial atmosphere; Shanghai is the most prosperous and modern city; Shenzhen is the second prosperous city and the youngest city; Suzhou, known as the East Vines; Dalian is the cleanest city in China. Chengdu is the most leisure city. Chongqing is a mountain city and known as fog; Xi'an is the ancient capital of six dynasties. Xi’an, Chengdu and Chongqing are three major cities in the west. Nanjing has already been declining both in economy and culture, but the Chinese Department of Nanjing University is very famous for its good quality , it seems the third only after Beijing University and Fudan University(in Shanghai) Others are Guilin, Guiyang and Lijiang, slow rhythm, beautiful and also leisure.
If you are a gourmet, you would be very disappointed in the north. Anyhow, you can have all dishes of China in urban cities, but it’s much expensive. And the obvious difference between the north and the south on food is Northern people like food made of wheat and barley such as pasta, dumpling(Jiaozi),steamed bread and southern people like food made of rice and other multicolored dishes/ cuisines. People in the east and southeast cities like seafood. I’m living near Chengdu and Chongqing; we love spicy food rice, especially spicy hotpot.
If you choose only one, it's Beijing. Two, Beijing and Shanghai, Three, history: Xi’an, Gourmet-Chengdu(Spicy food-Chongqing), scenery- Lhasa, culture& scenery of Han-Suzhou, study Chinese-Nanjing(less expensive than in Beijing and Shanghai).