Yes implement it as a heirarchical taxonomy. Have your countries as the top level terms, then states, then cities. Your URL structure will naturally reflect this. I would advise against /city/state/country, as it is illogical and counter intuitive, and doesn’t make for a good heirarchy ( so bad SEO too ).
On your frontend, taxonomy-location.php should be your template. I’d strongly advise against using 3 dropdown lists, as it’s poor UI/UX and a pain to implement. Instead look at ecommerce sites and implement the drilldown list pattern of picking a country, then picking a state on the next page, then a city on the next, letting users look on a country wide level or a state wide level or a city depending on how specific they want it.
The details of how to implement that however are beyond the scope of this question and answer, you will need to ask in another question