Select a map that is large enough to cover the paint damage on the wall. If you have an extensive collection of maps, you may have one that is suitable. If not, consider purchasing a new map or framing a map to increase its size.
Measure the paint damage with a tape measure to determine its center, and then mark the center with a pencil. It's important to hang the center of the map over the center of the paint damage to ensure that it is completely covered.
Hold a laser level against the wall. Mark a horizontal line directly over your pencil mark. If the map is large enough that you require two separate nails for hanging it, make two more pencil marks equidistant from the center mark.
Decide if you'll use a nail or screw to hang the map. If it's heavy, screws with anchors are the best option. If the map is light, you can safely hang it with a nail.
Hammer one or more nails into the designated marks on the wall. If you choose to use screws, make a small drill hole in your pencil marks, and then hammer an anchor into the hole. Use a screwdriver to drive a screw into the anchors, and then hang the map.