It's much more of a under the surface bustling with activity type of place.
When/If you decide to move here (or were born here) you have to actively search out things to do.
Especially on rainy days.
Museums tend to fall into that category.
The Asian Civilisations Museum is one option.
It's very heavy on the history.
Because religion (especially Buddhism) is such a big part of Asia, it's rich in that aspect as well.
I found it a little dry, and don't think it would be child friendly... but then again going to school in the USA doesn't necessarily put a lot of emphasis on the history of Southeast Asia.
(I apologize in advance for the shoddy quality of the photos. The museum is dim and all I had was my phone.)
The museum might be a good place to stop by and cool down if you're making your way around Boat Quay. I don't think it's a full day activity however.