China in 2-3 days
Beijing is your best bet for a quick taste of China. Start with Tiananmen Square, Mao Zedong Mausoleum and the Forbidden City, the North Sea Park and lake, and the nearby hutongs (the winding alleys of atmospheric traditional homes). The Temple of Heaven Park and the Summer Palace are also worth seeing. Under no circumstances miss the Great Wall — you’ll never forget how spectacular it is. It’s only an hour or so from Beijing, but even if you’ve only got two full days, allocate a full day to ramble along it. The wild wall (ie not a bit that’s been tarted up) at Huanghua is particularly spectacular.
China in 7-9 days
Combine two to three days in Beijing (ensuring you allocate one for the Great Wall) and two to three days sampling the sights and sounds of Shanghai. For a break from the big city, stop off en route to climb Tai Shan, the holy Taoist mountain, or take a day/overnight trip from Shanghai to the famous gardens in Suzhou or canals in Zhouzhuang.
China in 2 weeks +
A combination of flights and overnight train journeys should ensure you can see quite a bit in a couple of weeks. After Beijing and/or Shanghai, fly to Chongqing (it’s a long way west), the starting point for trips down the Yangzi River and through the Three Gorges Dam. From the end point you can catch an overnight train to Guilin, from where it’s an hour to the justly-popular Yangshuo, a backpacker mecca where you can chill out amid gorgeous scenery. You could then wind your way slowly down to Hong Kong, or train it back to Shanghai. The Terracotta Warriors in Xian are spectacular, but are not worth going out of your way for unless you’re on an extended stay in China.