How to run following a song through dark shifting streets?

In my setting, the streets of a city change every evening by Architects. However at night the song of the empresses murdered daughter wanders the streets. The party have learned that, order to find out how to take down the empress, they need to follow this voice. The Architects will be actively shifting the city as the players are outside, perhaps even making them unable to find their way back to the safehouse.

How would you go about making this engaging?

This campaign is hex crawl based, so I was considering having the route clearly laid out to them on the map and encountering something in their way each tile, but that seems too much like the day time exploration.