Singapore Art Museum
Modern art from both Singapore and the region. The permanent collection is lackluster, but exhibitions can be interesting. Guided tours in English at 11 AM, 2 PM.
Istana
Completed in 1869, this Malay-Indian hybrid building was once the Government House of the colony of Singapore, before being repurposed on independence as the official residence of the President. The 100-acre grounds occupy some of Singapore's choicest real estate and incorporate several gardens and even a 9-hole golf course. There is a Change of guard ceremony every first Sunday of the month. The Istana is open to the public on only five days a year: Chinese New Year, Deepavali, Hari Raya Puasa, Labour Day and National Day.
2902 Gallery
The largest dedicated photo gallery in South-East Asia, with a focus on Singaporean talent. Hosts changing exhibitions including the yearly Singapore Int'l Photography Festival (http://sipf.sg/) plus workshops, lectures and more.
Battle Box
The former HQ of the British army during World War 2, now turned into an air-conditioned museum complete with animatronic figures retelling the events of the days before surrender. Nearest MRT station Dhoby Ghaut, but it's a steamy hike up the hill.
National Museum of Singapore
Formerly Singapore History Museum, recently refurbished from top to bottom with a new wing added. The star of the show is the permanent Singapore History Gallery, a 2800 sq.m. multimedia extravaganza covering six centuries of island history, navigated with a super-flexible, if occasionally somewhat confusing, interactive audio guide system that lets you choose the events and items to focus on. There are also four Living Galleries focusing on food, fashion, film and photography, plus various temporary exhibitions and a few nice cafes and restaurants.
epSITE
Also known as the Epson Imaging Gallery, this small space features changing photography exhibitions. Hardly worth a detour, but take a look if you're in the area.