If your idea of a true nature adventure is to trek for hours on end, always running the risk of getting lost, then Central Catchment Nature Reserve would probably come closest to satisfying you. This 2,000 hectare reserve is made up of the forests around the Upper Peirce, Peirce, MacRitchie and Seletar Reservoirs. You can enter the Upper Peirce forest via the Old Upper Thomson Road.
There's no admission fee, which also means there's no visitor centre and you are left to your own devices. Unlike the Bukit Timah Nature Reserve, though, the forests of the Central Catchment are secondary forests. You can hike for quite a long distance here, as the park leads right on to Bukit Timah Reserve and beyond. Bring a hat for protection from the blazing equatorial sun and lots of water.