Beijing is undoubtedly the No. 1 destination of tourists to China while Shanghai is fast catching up after successfully hosting the World Expo 2010. The Beijing–Shanghai High-Speed Railway started running in mid-2011 and takes only five hours to connect these two major cities of China (the normal train takes about 10 hours). You can find full details (fare, time-table, etc.) here. I have also included Xian as one of the top cities to visit in China for, as someone put it, not visiting Xian when one is in China is like visiting Egypt and not going to see the Pyramids. Hangzhou's Westlake is a sight to behold and Zhouzhuang's water city is not quite the same as Venise as the locals have the water right by their doorsteps! Though they are not places that you would go from far to visit, I am featuring them here as their proximity to Shanghai makes them really worth visiting (despite its fame, Suzhou is no longer what it used to be and the time spent going there is better spent on visiting either Hangzhou or Zhouzhuang, to my mind). I agree, one cannot do justice to a huge country like China by just citing a few places to visit but this is just my personal contribution. Other visitors will no doubt prefer to go to Guangdong, Hainan, Yunnan, Xiamen, Shenzhen, Guilin, Chengdu, Harbin, Wuhan...but then, the list is endless!
And what about Hong Kong, which technically is still a part of China (since 1997), despite mainland China's "one country, two systems" rule) and the strong objection by Hong Kong residents to be a part of China.
Oh before I forget. Anyone who has been to China will tell you that local tourists far outnumber foreign tourists in cities like Beijing, Shanghai and even Xian. You will often see groups of them being led around by the tour leader carrying a pole with a tiny flag at the top (sometimes it's just an umbrella!) What does this mean to the foreign tourist? It means that if you intend to travel by train from one city to another you have to be prepared for long queues (and I really mean LONG queues that can take hours on end) especially during school holidays and Chinese festivals. Luckily in the major cities there are travel agencies who, for a small fee, will take care of the train booking for you. Whatever you do, don't try to stint on this. Unless you have a whole day to while away doing nothing but staying in queue with the massive crowds, I would strongly advise you to dig out a few yuans from your pocket and make use of their services to book your train ticket.
And, by the way, in addition to the usual words of greeting such as ni2 hao3 (Hello) or xie4 xie4 (Thank you) you would do well to learn how to say "don't want" in Mandarin which is bu4 yao4. This is indispensable in order to stop being pestered by street hawkers who will not take no for an answer.