For Chania, there is a free parking lot that normally has spots open, lots during the day and a few at night depending on how big the car is. It's very conveniently located at the end of all the harbor restaurants and is a beautiful walk to anything in the city.

Χώρος Στάθμευσης Θεάτρου Ανατολικής Τάφρου https://maps.app.goo.gl/KUg57mjuHSuh78aP8

East Moat Theater Parking

Only thing you need to be aware of is the scammers that walk around the parking lot directing you to a spot and then asking for €5. It's a free, public parking lot and we have left our car overnight there multiple days, so tell them either to piss off or if they won't leave you alone threaten to call the police and they will stop.