Stan Sesser's The Lands of Charm and Cruelty has a fscinating essay on Singapore and, as he puts it, "the fear that even the best educated Singaporeans feel towards their government." I started to notice very quickly that in Singapore - a clean, well-run city in marked contrast the inept dictatorships that mostly surround it - there was indeed an unpleasant climate of fear that business travellers must take account of. Don't press locals to discuss anything substantive outside of business. Don't be surprised if the Malayan and Indian minorities seem to be treated as second class citizens. Sesser's book has a lot of information.
Ian Buruma's The Missionary and the Libertine has a famous essay on Singapore, "The Nanny State of Asia" which any visitor should read about the police state climate of S'pore. Again this book helped me understand patterns and attitudes I began to experience while there. There is a lot about the Senior Minister, Harry Lee Kuan Yew, and his silencing of free speech. Buruma's other book, God's Dust, has another informative essay on Singapore.
Christopher Lingle's books, especially Singapore's Authoritarian Capitalism is a real eye-opener as to how S'pore works away from the tourist bureau explanations. You will understand the need for Western business's to "genuflect" to Singapore's leaders through their company's marketing departments in order to continue doing business there.
Chinese writer Bo Yang's The Ugly Chinaman and the Crisis in Chinese Culture gives an in-depth account of the underbelly of Chinese culture, very useful guide for families going to live in the Lion City. The book traces the sad story of repression in Chinese history by China's own leaders, the tale of worshipping the past to the exclusion almost of critical thinking, and how this has led to certain unpleasant aspects of modern Chinese society - rude crowds, obsession with not losing "face", greediness. Bo laments all this, but he is anxious to help Westerners understand why Chinese crowds and shopkeepers (and leaders!) are rude and pushy, blow their noses in public, are xenophobic. A helpful book that leads to clarity, and a more postive appreciation of things Chinese.
Lastly, Paul Theroux's Saint Jack, though a novel, capture's well many attitudes of locals and long-term expats in the city. I found it a remarkably accurate take on the place, though fiction.