We mainly book at places that allow cancellation up to 6pm local time on the day of arrival.
Once, we booked a hotel upon arrival at ICN, and another time, we booked ATH once cleared at JFK(Flight had less than 20 open seats).
We have become a huge fan of Airbnb lately, but the cancellation policy is pretty strict, so we only book those if the flight is wide open.

Nothing is safe though, as you could even have full fare tickets and have a flight cancel.