Where are some of the coolest places in Singapore to bring a 9 month old baby besides the usual tourist attractions?

It depends on what kind of places you want to bring your 9months old. As they are still young and don't understand much things. You can consider bringing them to indoor playground. Cool de Sac http://cooldesac.com.sg/ Polliwogs http://www.thepolliwogs.com/display/news.asp?NAVID=1886 You can also try bringing them to the beach, allowing them to feel the sand and water splashing onto them.