It absolutely depends on the scale of what you're doing too. It seemed like you might be walking on a much more macro scale than most roguelikes, which means walking from one place to the other might be up to an hour. Most roguelikes on a more microscale would take maybe 10s to go from one tile to another.
Either way, get a decent turn/time ratio, and then you can convert from one to the other. You can simply update the time representation in hh:mm:ss whenever enough turns have passed to reach the next second

And of course, you can make this as macro or micro as you want. Perhaps you'd only have "Hour hh of dd/mm/yyyy"

Of course, then it's important to have a system where you don't have to iterate turns one by one, but can simply skip to the next "activation" of any entity on the map.