Sex between males is illegal in Singapore, carrying a minimum sentence of 10 years. In reality, nobody is ever likely to be prosecuted, but the ban remains as a symbol of the government's belief that the country is not ready for the open acceptance of 'alternative lifestyles'.
Despite that, Singapore has a string of popular LGBT bars. A good place to start looking for information is on the websites of Travel Gay Asia (www.travelgayasia.com), PLUguide (www.pluguide.com) or Utopia (www.utopia-asia.com), which provide coverage of venues and events.
Singaporeans are fairly conservative about public affection, though it's more common to see displays of familiarity among lesbian couples these days. A gay male couple doing the same would definitely draw negative attention.