I'm trying to get a list of all the Hungarian city names from google maps, but I don't know how. Is this at all possible?
As far as I know, there is no such possibility. Although Google Maps API lets you determine the name of the location by its coordinates (the Reverse Geocoder API) and lets you find coordinates of places that match the given name query (the Geocoder API), I'm pretty sure that it won't let you get all objects that match a certain criteria.
So the short answer is: no, it's impossible.