Perhaps you can look at this and see how to adapt it to display multiple points on the same map
points = {};
For[i = 1, i < 6, i++,
point = Input["What are the {x,y,z} coordinates?"];
AppendTo[points, GeoMarker[GeoPosition[point]]];
];
GeoGraphics[points, GeoRange -> "World", GeoProjection -> "Robinson"]
Note: You enter those x,y,z coordinates inside braces, like this,
{13, 25, 37}
for each point
