If I understand you correctly, the mechanism you're going after is effectively this:
https://en.wikipedia.org/wiki/South-pointing_chariot
It's ancient technology, but I'm sure the principles at work hold true. However, I'd be cautious with this design, as any slippage of the wheels while going over obstacles will introduce some amount of drift from the original direction.
I can't think of any other design that won't require sensor input. Your idea of floating in water has its problems aside from legality, seeing as any jostle will start it spinning. I don't see any use for a cylinder which points a certain direction but can't affect anything else.
I'm interested why you don't want to utilize a gryo/other sensor, seeing as they're by far to most mainstream way of monitoring direction.