What is the best aspect ratio for a geographical map when considering ease of finding a route from a variable start point to a marked end point?
A circle with the user's current location at the center.
It places no constraint on the user's choice of direction. Most likely your application is screen based and thus for restrained by some type of square display. The best aspect ratio obviously depends on the device and screen real estate and how it is used and navigated.
In this case, i think the zoom level of the map is a much more important factor than the aspect ratio of the map itself. So long as the map fits nicely on the page and is big enough to be pinchable on the average smart phone i think you're in good shape.
A good example is built into google maps. When you select a bus route to a certain location, the map starts on what you were last looking at, waits for a second, then zooms out just enough to fit both the starting point and destination in the map (with a little bit of margin). Note that the map centers between the you and the destination.