Most playgroups for kids this age are mom-accompanied programs. My son goes to Busy Buddies twice a week at UE Square and totally loves it. I think its the best toddler programme I have seen in Singapore. They do a bit of everything - singing, dancing, storytelling, a bit of arts, introduction to letters, rhymes, life skills etc. Their website is
www.busybuddies.com.sg If you want just pure physical fun, consider JWT Kids again at UE Square. I take him there once a week and he has a blast! Another good place is Growing Up Gifted at United Square. Good programme but their rooms are too small and my son refused to be locked in a small place.
Hope this helps.
MM