With over 500 million users on it, Sina Weibo is a good place where you can learn what is going on in China and what Chinese people are talking about. It was launched in 2009, and has been growing fast during the past three years. On Weibo, People are always discussing about breaking news, especially those that mainstream media do not report because of censorship. I found their hot topics page very useful. On this page you can search for news either by content (social, financial, political, sports, fashion, entertainment, etc) or by date. I like using Weibo because information and news are updated very fast on it, and you will get to know what is going on even before you hear from any news media.
South China Morning Post is the first and one of the most famous English-language newspaper in HongKong. The newspaper is published in HongKong and not directly controlled by Chinese government, so that it has less bias when reporting news in China. The home page is clear and the sections are easy to follow. There are very few advertisements since it charges about $2 a week for subscription. There is also a Chinese-language website for the paper, but the contents are not as good as in the English version, which is what I hope they could improve a little bit.