entity = RandomEntity["Country"]
cities = CityData[{Large, CanonicalName @ entity}]
Manipulate[DynamicGeoGraphics[{GeoMarker[cities], GeoPath[{x, y}, "Geodesic"]}],
{{x, First @ cities}, Thread[cities -> CommonName /@ cities], ControlType -> PopupMenu},
{{y, Last @ cities}, Thread[cities -> CommonName /@ cities], ControlType -> PopupMenu}]