You can access the Dairy Farm Nature Park from the Hillview MRT station. If you drive, you can park at Car Park A off Dairy Farm Road and move towards MOE Adventure Centre.
When you take the right road from the MOE Adventure Centre, you can walk towards the Singapore Quarry. It is about 20 minutes walk. This Singapore Quarry is worth a visit. It is tranquil and there are fishes (Carps and Arowana fish and others) in the water. Visitors do yoga and stretching exercises at the viewing deck. Or you can just sit and enjoy the peace of the place.
On returning back to the MOE Adventure Centre, you can take the left path towards Wallace Trail. There is a Wallace Education Centre before the trail. Wallace Centre is named after Alfred Wallace in honour of his contribution to Natural Science (1854).
The Wallace Trail takes you into the forested area and you can cover the loop in less than an hour.