After walking through the giant body at the Singapore Science Centre, I took a 15 minute walk down the street to the Chinese and Japanese Gardens.
My interest in gardens can probably be traced to my childhood; my grandmother and my mother both had gardens in their backyards, and I have distinct memories of visiting public gardens like the Japanese Garden in San Francisco's Golden Gate Park. Singapore's gardens are quite expansive, set up on the same gigantic tract of land as the Science Centre and its accompanying museums.
It would have been nice to have had clear or nicely cloudy skies, but I saw all I wanted to see on this trip so once the rain stopped I walked back to the nearest MRT station to take me to my next stop.
The Chinese Garden MRT station leads right to the east entrance of the Chinese Garden. There is a bridge between the Chinese and Japanese gardens, plus additional west entrances for both gardens. Walking to/from the Science Centre takes 15-20 minutes despite being right next to each other due to the layout of the gardens and the size of the park.
The park is open daily 6 AM to 11 PM, and admission is free. The Turtle and Tortoise Museum doesn't seem to be worth the approximately $5 entry fee but I haven't been inside to verify anything. However, it's open 9 AM to 6 PM.
Keep in mind that the renovation works should be completed by mid-2016. Until then, expect various attractions to be closed.