I'm not obviously saying there were no atrocities in Shanghai or Beijing or any other city (there were obviously plenty), but Nanking does stand out in terms of scale and in people's memory. Was it just because Nanjing was the capital of Nationalist China? Or was there more to it?
The legacy of the Nanjing Massacre, or Rape of Nanjing is one that has become mired in politics in more contemporary times. That's not to downplay the significance of the massacre or the horrible atrocity that it was, but simply its legacy has more to do with political posturing than the event itself.
Before discussing the legacy, however, it should be noted that while you could argue that massacres took place across China outside of Nanjing, the scale and actions of these do not rival Nanjing. What's the difference between a Japanese officer indiscriminately shelling a city with artillery, killing thousands, and officers ignoring their troops plundering and raping a city? They both result in a lot of death and misery for the unfortunate citizens caught in the middle, but ethically at the end of the day they're both immoral actions. But there is a difference between the two actions. One is an overall strategy towards a war goal that can be passed off as the nature of war, while the other is action is a blatant example of the unnecessary, but sometimes real, consequences of a war fueled by ethnic and nationalistic tensions between two countries.
Why Nanjing?
Nanjing, like other treaty port cities in China, had a fair amount of foreigners. Probably not as many as Shanghai, but more importantly due to its political significance, many Western ambassadors and humanitarian NPOs had offices here. When the Japanese reached Nanjing, Chiang and his officers wanted to hold out for as long as they could, and just like in Shanghai, Chiang was one of the last officers to be lifted out of the city before it fell (at his own request). Obviously, losing Nanjing was a big political victory for Japan, but Chiang knew that he could continue falling back West, and wanted to begin a scorched earth tactic to fight the superior Japanese. This evidently irritated Japanese general Iwane Matsui, who earlier had demanded Nanjing surrender or be shown no mercy. Keep that name in mind, it'll be relevant in a little. After taking the city, the massacre obviously began.
The Japanese generally made good on their promise to keep Westerners from harm in China. This gave Western journalists, photographers, and other travelers who came to China to report on the war and got stuck in Nanjing the liberty to roam around and take pictures of the massacre that followed, resulting in plenty of evidence. American John Magee, an Episcopal priest and amateur filmmaker, was present during the massacre, and his film is available. You can go on Wikipedia and look at some of these in the "Massacre" section, I won't link them since some are NSFL, but if you're interested, they're there. This evidence was made widely available after the war, especially during the trials in Japan that the US held. Iwane Matsui himself was sentenced to hanging.
The Legacy of the Massacre
In the post-Mao world of East Asia, China's detente with the West has made Japan lose its superior trading position among Western nations. But, Japan still plays an important strategic and economic role in East Asia, especially for America, and the past few decades have been riddled with Chinese-Japanese relations jumping back and forth between "Good and Bad." The Massacre is still a symbol of mistrust for many Chinese citizens, and this has allowed the CCP to make good use of it politically when seeking international sympathy. Takashi Yoshida explains the role the Massacre plays in the collective memory of Chinese, Japanese and US citizens. He argues that China wished for Japan to admit their atrocities, but Japan, due to a combination of nationalist pride and viewing themselves as victimized by the US Atomic bombs, refuses to see it the same way. The US, acting as a mediator, has attempted to solve these issues in years past, but to little avail.
To further complicate things, it has been something of a tradition for Japanese PMs to visit the Yasukuni Shrine, a place of remembrance for fallen Japanese officers and troops from the Boshin war, to WW2. Remember Iwane? Well, he and several other convicted war criminals are enshrined there as well. The pilgrimages to this site has drawn criticism from both China and South Korea in years past. PM Junichiro Koizumi's pilgrimage to the shrine as recent as 2006 drew considerable criticism internationally, with the Chinese Foreign Ministry claiming Koizumi was "wrecking the political foundations of China-Japan relations." South Korea also protested.
Japan's insistence on ignoring the "Nanjing Question" has thus made it an easy target for Chinese nationalists. While they admit to the massacre taking place, many Japanese have contested the actual number of deaths (which isn't officially known). Most academics place it around 100-300,000, while Japanese figures have been significantly lower.
In 1985, the Chinese government created the Nanjing Memorial Hall, a pretty large museum dedicated to the victims (well worth a visit as well). It even includes a section with the skeletal remains of victims. The Rape of Nanjing also has a considerable amount of media dedicated to it, particularly in books and films. Not all of it is sympathetic to the Chinese view. In 2007, Japanese filmmaker and nationalist created The Truth about Nanjing, a documentary intended to "dispel the propaganda surrounding the Nanjing Massacre;" the film makes many controversial claims. This isn't the only evidence of Japanese backpedaling; The Alleged "Nanking Massacre:" Japan's Rebuttal to China's Forged Claims by several Japanese authors goes as far as claiming the massacre doesn't exist. Iris Chang's The Rape of Nanjing is a bestselling book published in 1997, one of the first major English-language publications on the subject. It has been listed as the inspiration of several documentaries and films. But this book has caught the criticisms of academics for over-exaggerating the atrocities. It can be hard to find a lack of bias, as well as even ground, among both side's nationalists.
Conclusion
The Nanjing Massacre plays a big role in the psyche of both Japanese and Chinese nationalists, leading it to be much more frequently discussed in contemporary times. Its legacy lives on through a plethora of media, which has drawn criticism from academics as being biased towards either side. The opening of the Nanjing Memorial in 1985 has allowed the Chinese government to publicly harness nationalist sentiment for Chinese visitors at the cost of Japanese prestige, while the continued tradition of the Yasukuni pilgrimage is seen as a slight by many Chinese (and Korean) nationalists. Its a very touchy subject.
Source:
Yoshida Takashi, The Making of the "Rape of Nanjing" is a very good source on this (Columbia U Press, 2009).
Wikipedia's reference section is pretty good too, but keep in mind that there are many biased sources listed.