Right off North Bridge Road (and close to St Andrew's Cathedral and City Hall), and on my way to Fort Canning Park, close to the intersection of Hill and Coleman streets...
...there are three interesting sights. 1) The Singapore Chinese Chamber of Commerce building.
2) The Armenian Church.
This is the oldest Christian church in Singapore. It is built by G.D. Coleman, the architect of the Istana and St Andrew's Cathedral, between 1835 and 1936, although the original design that followed ancient traditions has been changed soon after.
There were only 12 Armenians in Singapore when the church was built, and the congregation never grew beyond a little above 100. But local Armenians were prosperous, and Armenian communities in Java and India, as well as local European and Chinese residents pitched in with funds to build the church. Armenians have made huge contributions to Singapore: the founders of the Raffles Hotel, and the Straits Times (the largest Singaporean daily), as well as the discoverer of the natural hybrid orchid that became the national flower of Singapore, were all Armenian.
(These two buildings are extra. One is Bacchanalia, a restaurant, the other one is the Singaporean Philatelic Museum.)
3. The central fire station. Although not the first fire station, because it replaced 3 former ones when it was opened in 1909, it certainly is the oldest fire station in Singapore.
As luck would have it, the Central Fire station has a weekend visit program, which means that every Saturday the station welcomes everybody between 9am and 11am. And I was there at 10.30!