There's always 'recreational mathematics' -- puzzles of the type Martin Gardner was known for.
On the less STEM side, taking a look at what's around you and trying to reverse-engineer the reasons behind design decisions is also useful. Why do zippers have that little nub on them? Why is jaywalking a crime? Why are red lights red rather than blue? Sometimes this is a matter of path dependence, but other times there's some deeper reason.