You could also try Gymboree in Tanglin Mall. I take my 12 month old and there are several others in that age range. There is also an 'open play' in the afternoon for nominal fee.
Have you been to Atlantis playground in the Delta Sports Complex on Alexandra Rd? It's kind of a 'no frills' indoor playground - but great place for this age as they can just crawl around and it's only $4 a go.
Also Go-Go Bambini on Dempsey Road. This is another indoor playground though a bit better for the older ones. That being said - I brought my 12 month old and my 3.5 year old there today and they both had a ball - the little one just crawled around the playhouse and the ball pit. Plus there are a lot of other moms there with the 1 year old crowd so easy to strike up a conversation. It's a bit expensive - but they have great coffee
There is also Kindermusik in Tanglin Mall. I haven't tried it yet - but have heard good things. There are also several kiddie programs in UE Square Shopping Mall.
Also there is the Jacob Ballad Children's Park in the Botanical Garden (it's the Khem Hock Road exit off Bukit Timah) - there is a water play area that the toddlers seem to love.
There are also Playgroups associated with different organizations - New Mother's Support Group, Stay At Home Moms, ANZA, AWA...etc.
Lastly, there is a soft play area at the Forum shopping center - it's $10 for a 2 year membership and the playground is open to the public at certain times - I think it may be 11 - 1 and then 4:30 to 7 - but you would have to check to be sure. They also open at 10 or 10:30 on Saturday and the kids love to go as it's not too crowded.
Oh, almost forgot - check out the aquaducks site:
http://www.aquaducks.com.sg/location.html for info on swimming.
Hope this helps!!
