Indeed, China has myraids of places of interest worth a visit. In line with your requirements, Beijing, Xian and Shanghai are the tourist destinations for those foreigners who pay their first visit to China. As for Beijing, as the capital of China,Beijing is a superb cobmination of modernization and profound cultural tradition. In the light of this, the following tourist attractions are highly recommended: the Forbidden City, Temple of Heaven, Mutianyu Great Wall, Badaling Great Wall, the Summer Palace. And if you are inclinded to experience the modernization of Beijing, you are suggested to visit National Center for the Performing Arts, Olympic Green where Water Cube and Bird's Nest locate. Definitely, there are countless alluring attractions in Beijing derseving your visit. It depends on how many days you will stay there. As for activities in Beijing, from my humble opinion, you will feel free to take an active part in various sorts of activities such as have a taste of palatable traditional Chinese food, Beijing roast duck in particular, or enjoy Beijing Opera, playing Kungfu and etc. It is also your option to decide whether to purchase some souvenirs like pearls and silk in the bustling and prosperous commercial streets.
As to Shanghai, the international metropilian city, typically attractive tourist destinations are Yuyuan Garden, Shanghai Museum where you will be speechlessly struck by marvelous Chinese history and culture via diversified antiques.Definitely, it is also very popular to pay a visit to the Bund, particularly at night to sense the prosperity of this metropolis. Other strongly recommended attactions include World Financial Center, People's Square, Xintiandi, Jade Buddha Temple and so on. you can watch acrobatics show, go to the bar to experience the luxury of Shanghai in the evening.
As to Xi'an, definitely, Terra Cotta Warriors, Shanxi History Museum, Big Wild Goose Pagoda and etc all worth visting. Chinese Dumplings are the most pupular among tourists. Maybe you can also have a try if you fancy.
Since I am also fanscinated with travelling, from my personal travelling experience, if this is your first time to travel around China and especially last as long as 20 days, the following tourist destinations are also as splendid as the above listed ones:
Guilin known for its karst landform and exotic picturesque natural sceneries under the sun, it really deservs your travel. Tibet is also a great place for your visiting for its sacred buddhism spirit and its complicated but abrupt canyons, precipitous mountains as well as luxurious virgin forests. Hangzhou typically renowned for West Lake, Suzhou known for its unique gardens all worth visit.
As for the itinerary, it depends on where you will land, Beijing or Shanghai, then to make the most appropriate itinerary for youself. Hope the above information will be helpful and wish you a happy travel in China.
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