Sights in Singapore are covered in more detail under the various districts. Broadly speaking:
Beaches and tourist resorts: Head to one of the three beaches on Sentosa or its southern islands. Other beaches can be found on the East Coast.
Culture and cuisine: See Chinatown for Chinese treats, Little India for Indian flavours, Kampong Glam Arab St for a Malay/Arab experience or the East Coast for delicious seafood, including the famous chilli and black pepper crab.
History and museums: The Bras Basah area east of Orchard and north of the Singapore River is Singapore's colonial core, with historical buildings and museums.
Nature and wildlife: Popular tourist attractions Singapore Zoo, Night Safari, Jurong Bird Park and the Botanical Gardens are all in the North and West. Finding "real" nature is a little harder, but the Bukit Timah Nature Reserve located in the same district as the zoo has more plant species than that in the whole of North America. Pulau Ubin, an island off the Changi Village in the east, is a flashback to the rural Singapore of yesteryear. City parks full of locals jogging or doing tai chi can be found everywhere. Also check out the tortoise and turtle sanctuary in the Chinese Gardens on the west side of town for a great afternoon with these wonderful creatures. $5 for adult admission and $2 for leafy vegetables and food pellets.
Skyscrapers and shopping: The heaviest shopping mall concentration is in Orchard Road, while skyscrapers are clustered around the Singapore River, but also check out Bugis and Marina Bay to see where Singaporeans shop.
Places of worship: Don't miss this aspect of Singapore, where Buddhism, Taoism, Hinduism, Sikhism, Baha'i faith, Christianity, Islam and even Judaism all exist in sizeable numbers. Religious sites can be easily visited and welcome non-followers outside of service times. Particularly worth visiting include: the vast Kong Meng San Phor Kark See Monastery near Ang Mo Kio, the colourful Sri Mariamman Hindu temple in Chinatown, the psychedelic Burmese Buddhist Temple in Balestier and the stately Masjid Sultan in Arab Street.
If you are traveling to Singapore, be sure to carry the following:
Sun Glasses - Singapore is usually bright and sunny.
Umbrella - Be sure to carry an umbrella in your luggage,as there is some precipitation throughout the year. However, the rain does not last long usually.
Sun block - If you plan to go out during the day time, it is advisable to apply sun block as it is mostly sunny throughout the year.
Shorts/Half Trousers - Singapore can get real warm. Although air-conditioning is available in all public transports except a few public buses and almost all internal areas, it is advisable to carry some light clothing. Do note that some places of worship may require visitors to dress conservatively.
Flip-flops - Singaporeans love to wear flip-flops. Be sure to carry a pair, just to blend in. Try sandals if you're not used to flip flops, but beware - in some formal establishments e.g. catching a show at Esplanade no flip flops, sandals, or shorts are allowed.
Sweater - the malls and museums' air conditioning can get cold, though usually this is a welcome relief from the heat.
Mosquito repellent - day or night, they're lurking. Dengue fever is a particular problem in this part of the world, so stay protected.