Here's a little advice, but not much more than that:
If you want to find places by name, or name prefix, as you indicate that you wish to, then you would be ill-advised to set up a data structure which stores the data in a hierarchy of country, region, town as you suggest you might. If you have an operation that dominates the use of your data structure you are generally best picking the data structure to suit the operation.
In this case an alphabetical list of places would be more suited to your queries. To each place not at the topmost level you would want to add some kind of reference to the name of its 'parent'. If you have an alphabetical list of places you might also want to consider an index , perhaps one which points directly to the first place in the list which starts with each letter of the alphabet.
As you describe your problem it seems to have much more in common with storing words in a dictionary (I mean the sort of thing in which you look up words rather than any particular collection data-type in any specific programming language which goes under the same name) than with most of what goes under the guise of geo-coding.
My guess would be that a gazetteer including the names of all the world's towns, cities, regions and countries (and their coordinates) which have a population over, say, 1000, could be stored in a very simple data structure (basically a list) with an index or two for rapid location of the first A place-name, the first B, and so on. With a little compression you could probably hold this in the memory of most modern desktop PCs.