If the map is actually a photo with notations, I'd either get rid of the grid in the background, or make it an overlay (hand drawn, maybe?). Or maybe just hint at a grid with crosses in four corners as if it were a military recon picture (check images of the moon landing to see what I mean with "crosses").

Oh, and I'd hint at perspective with the help of shadows, and then make it greyscale (sepia colour in old photos is a result of the materials used to capture light, and not a result of aging).