The capital, Beijing, is second in population, 8 million in the urban area (almost identical to The Big Apple's number), about 13 million in Greater Beijing. The latter takes up about 6,336 square miles, more than 20 times New York City's mere 304 square miles. (Beijing's urban center area, however, is only 77 square miles, according to its official English language website.) As a destination, though, Beijing beats its competition hands down, and if you can see only one place in the nation, this is it.
The must-see list is short, but impressive enough. At the top is the Forbidden City, home to China's rulers since 1420, and once thought to be the center of the world. (China's name in Mandarin is "Central Country/Kingdom," after all.) Next is Tiananmen Square, the world's largest public square (about 90 US football fields or 99 acres), where you can skip Chairman Mao's Mausoleum as far as I am concerned. Then comes the Temple of Heaven (same dates as the Forbidden City) and finally, the Summer Palace (1749-1764, last rebuilt 1903). If you can find any of the fast disappearing Hutong (alleys), go see them, preferably by foot. Also a must: a side trip to the Great Wall (begun c. 453-221 B.C.E.), where you have several options as to the section you wish to see. Most popular (and crowded) is Badaling. En route to the wall (or coming back), be sure to see the Ming Tombs (1368-1644), where 13 of the Ming emperors are buried.
Biggest in population is Shanghai, boasting over 13 million people, with an area of around 2,418 square miles (half the size of Connecticut). Though I live in Manhattan, the first time I saw Shanghai's massive Pudong district with its dozens of new skyscrapers, I felt a bit like a provincial hayseed seeing what a Big City really can look like.
Highlights of Shanghai, in addition to Pudong, include: a visit to the Shanghai Museum, which I think one of the world's best and many consider China's best; The Bund, where you can promenade past more than 20 colonial era buildings (most 1897-1937) along the Huangpu River at this eastern end of the old Shanghai; the lovely Yu Garden (1577); the Jade Buddha Temple(1918); the Confucius Temple (1855); the Shanghai Museum of Arts & Crafts (c.1910); the Huxinting Floating Teahouse (1784); and the Peace Hotel (1929).
Biggest in area, ludicrously so, is the city of Chongqing (formerly Chungking), which spreads out over a massive 31,768 square miles (a bit larger than South Carolina). Don't ask why the city is so big, even locals argue about how this happened. Though there are "only" around 7 million in its urban area, the figure for the entire "city" is closer to 31 million, but that should relate more to what a province would have in population, not just its urban center. The center is most unlovely, with few tourism targets, but is a jumping off place for China's Far West, even Tibet. (To put areas in perspective, Los Angeles proper has just 498 square miles.) Chongqing became capital of China during World War II after the eastern part of the country was occupied by Japanese troops.
I can recommend only two spots, the Artists' Village and General Stilwell's House. At the first, you'll find as the village's base a group of 17 charming cottages in which state-chosen artists live and work, and their wares are on sale. At the former residence of General Joseph Stilwell, you can see relics of the hero of the Burma Road, who was sent here during World War II to liase between President Roosevelt and the Chinese Nationalist leader, Chiang kai-Shek.
The fourth largest city here in terms of population is Tianjin, with over 5 million inhabitants and 4,200 square miles in area. Just 90 miles east of Shanghai, it was an important colonial city, especially from 1861, when areas were conceded to many foreign governments for their business purposes. First came the British and French, then the Japanese, Russians, Americans and others.
Today, you can see remnants of eight Foreign Concession neighborhoods, but the highlights here are the 2004 Tianjin Museum (said to be one of China's largest public buildings, with an impressive design but the exterior best seen at night) and the Old City, especially the Guangdong Guildhall & Theater Museum (1907).
China's fifth largest mega city is Wuhan, a busy industrial center 700 miles west of Shanghai at a bend in the Yangtze, which turns south for a bit here. Most foreign tourists begin or end their Yangtze River cruises in Wuhan, their previous or next stop being Shanghai.
Highlights here: Hubei Provincial Museum, with possibly world's oldest musical instrument (65 bronze bells), the Guiyuan Buddhist temple (early 20th century), and Chairman Mao's Villa (1958), where he hosted President Nixon.