There are an infinite number of points on the earth's surface where this is possible.
The simplest to explain is starting and ending at the North pole.
Now imagine a circle with a circumpherence of one mile drawn around the south pole. Now start one mile North of that circle. Walking 1 mile south will bring you onto that circle. Walking one mile east will take you round the circle exactly once and then i mile north will take you back to where you started.
Now consider a circle around the south pole with a circumpherence of half a mile. The same will apply, but this time walking east will take you exactly twice round the circle before returning north to the start point.
This can be repeated with circles 1/3 mile, 1/4 mile, 1/5 mile . . . 1/nth mile in circumpherence.