Two weeks to a month in China
Ten days to a month in China is a general Chinese itinerary with a scope varying by travel time.
China is too large a country to realistically "see" in one trip; most travellers should plan multiple trips if they hope to see a broad swath of the nation or a trip to only one region if they only have time for one tour. Alternatively, they can use China's long-distance rail system to hit up China's "hot spots" - Beijing, Shanghai, Hong Kong, Xi'an, maybe the Yangtze River or Yunnan for some nature - in one swoop. Travellers might want to do some research to find which areas or aspects of China appeal most to them, then focus on those.
This itinerary is layered so that travellers can add successive regions to their trip as time allows. It starts with the north, then later sections explore other regions.
China is easily travelled via its extensive rail system, yet remember to book tickets in advance due to infrequent trains.
There is also an extensive internal airline network, generally quite good and moderately priced. Flight delays are moderately common, especially at peak season. Prices on internal flights are often significantly better if you buy tickets in China rather than from an agency or web site elsewhere.
Traveling by bus is also possible; buses tend to go more places than trains and are often a bit cheaper. In the more modern and prosperous areas, or even on major routes in more rural areas, they are generally quite good. However, the quality does vary a lot; the worst of them are crowded, noisy, dirty, and unsafe.
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 Ten days to two weeks: North China Plain
This area is the heartland of Chinese civilization and rich in history. It remains China's most densely populated region and therefore a good place to explore Chinese rural (or urban) daily life if you have time to spare. The Yellow River is the primary conduit through the area; see the Along the Yellow river itinerary for more details.
Up to a week should be spent in the area around Beijing, China's capital and in many ways principal city.
Beijing itself can probably be seen in four days. Reserve your first full day for the various sites around Tian'anmen Square, including Mao's Mausoleum, the Forbidden City, and maybe some quieter areas nearby, such as Jingshan or Bei Hai Parks. Tour some of Beijing's temples on the second day, especially the Temple of Heaven, and visit some historic hutong neighbourhoods. Visit the Summer Palace on Day 3, combined with the Olympic buildings. Visit the Great Wall and Ming Tombs before leaving. Try to factor in some shopping (or browsing) in Beijing's historic shopping districts south and east of the Forbidden City and a performance of Beijing opera or acrobatics. Beijing is a city of many attractions, so feel free to linger if you so desire.
On the next day move on to Chengde or the closer Tianjin. Then take a train to Shandong and allot two full days for a hike up Mount Tai and a visit to Qufu. Consider making a detour to Qingdao if you have the time.
The must-see attraction in nearby Henan are the Longmen National Park outside of Luoyang. But this area was the political center of China for many dynasties, so seek out the scant historical relics in Luoyang and Kaifeng - or just settle for the Henan Provincial Museum in Zhengzhou. Anyang, China's capital in the 2nd millennium BCE, is for the hardcore history buffs. Use provincial capital Zhengzhou as your base.
Xi'an was also a longtime capital. Although stocked with historical sights of its own, including the Big Goose Pagoda, city walls, mosque, and Shaanxi History Museum, the key attraction here is the Qin Emperor's Terracotta Army outside town.
 Two weeks to a month: Yangtze Valley
If you have more time, it would be a good idea to explore China's second major valley: the Yangtze through the center of the country.
From Xi'an take a train to Chengdu. This is the capital of Sichuan and a center of high culture, including teahouses and Sichuan opera. Be sure to visit the Panda Breeding Center outside of town, and maybe Du Fu's (China's most important poet) cottage. The most important day trip from here is to Leshan, home of the world's biggest Buddha statue, carved into a cliff overlooking a river. You can also visit the Sanxingdui Museum and learn about another locus of early Chinese civilization, or visit the archaic towns of Zhaohua and Langzhong (although these entail long bus rides that might not be worth it).
From Chengdu move on through the densely populated Sichuan Basin to Chongqing. There is enough here for a day but it is mostly significant as a jumping-off point for the essential Three Gorges Yangtze boat trip. A leisurely voyage up the Yangtze's many tributaries is well-advised. The final destination is usually the Three Gorges Dam at Yichang, but continue on to Wuhan by boat or train. This is another big city with about enough to see for a day - the provincial museum, the headquarters of the Wuchang Uprising which eventually toppled the empire, and the European architecture of Hankou.
If you're interested in seeing more Chinese scenery, a worthy next trip could be Mt. Lu and Huangshan, especially the latter in southern Anhui, but they both require extra time - at least two days from Wuhan - so only consider visiting if you can budget enough time.
Otherwise, finish your trip with a visit to the handful of important and interesting cities on the lower Yangtze. First off is Nanjing, perhaps best known for being the site of Japan's massacre in 1937 but also an old imperial and Guomindang capital. Must-see sites include the old city walls, Purple Mountain (the tomb of Sun Yat-sen), the massacre memorial, and the museum to the Taiping Rebellion. After a day or two here, proceed to Suzhou, an old canal city with many traditional gardens, pagodas, and traditional neighborhoods and city streets. Hangzhou is also an essential visit: its West Lake is one of China's all-time great scenic spots and an important landmark for the Chinese.
Finally, try to set aside two days at least for the huge city of Shanghai. A walk along the Bund is mandatory, but also consider taking a boat trip up the Huangpu to the Yangtze to get a good view of the modern architecture on the other bank. Shanghai also has one of China's best art/cultural museums, and the Yu Gardens & Bazaar are worth a walk through. Finally, Shanghai has many minor historical sights from its pre-PRC days and some of the nation's best shopping.
Most tourists probably won't have more time to travel; but if you have the extra time, money and/or energy, or are making a return trip, there is more to see.
South of Shanghai is the island of Mount Putuo, a sacred yet balmy getaway that might be worth a day trip from nearby Ningbo. Further south down China's coastline are the provinces of Fujian and Guangdong, China's main maritime trading zones and the source of most Chinese emigrants. The main attraction in Fujian is the port of Xiamen, an old colonial city with many European-style buildings, a memorial and statue of Koxinga, and an Overseas Chinese Museum. You can also head inland to the Yongding area, where you can see giant Hakka earthen dwellings scattered around the countryside. Guangdong is one of China's burgeoning economic hubs, and is dotted with huge and growing cities. Guangzhou is the oldest of these, and is noteworthy for its Sun Yat-sen Memorial Hall, its cuisine, and other European island. Shenzhen is probably the world's newest major city and has several bizarre theme parks (Splendid China, Minsk World, Folk Culture Village) and legendary shopping.
The big destinations are the special administrative regions of Hong Kong and Macau. Spend a few days in Hong Kong drinking in the view from Victoria Peak, cruising the harbor on the Star Ferry, sipping tea at the Peninsula Hotel and perusing the street markets. Lantau and Lamma islands make for relaxing and scenic day trips. Macau is mostly noteworthy for its gambling and unique Sino-Portuguese culture and history. See A week near Hong Kong.
Beyond Macau, there isn't too much to see, but if you continue west far enough, you will reach the western province of Guangxi, gateway to China's rugged southwest. This is an adventure destination popular with backpackers, home to scenic wonders like the Li River and Tiger Leaping Gorge, quaint old towns like Lijiang and Dali, and ethnic-minority strongholds like Xishuangbanna and the Hmong villages of Guizhou. See Yunnan tourist trail.
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Other corners of China worth seeing on subsequent trips include: