Recently I was working with a landscape architect on a labyrinth project for a memorial garden at a church and there was a question of which direction the labyrinth should face. So let me share what I've learned while building and consulting on hundreds of projects.
There are many schools of thought regarding the orientation of a labyrinth. Many Christians say a labyrinth should face east, based on the idea that churches were built with their altars in the east. The prime example that's usually given is the famous labyrinth at Chartres Cathedral outside Paris. Interestingly, the Chartres Cathedral labyrinth does not face the east. It is actually oriented 42 degrees off the east-west axis, just as the cathedral housing it is off-line. The cathedral is only the latest building on an ancient site, and re-orienting it would have been impractical.
Generally when we're deciding how to orient a labyrinth, we believe it should be designed so that you are facing the vista or land feature you find most calming while standing at the entrance to begin your walk. Personally, I think this is comforting and enhances the walker's experience because the only decision you have to make as you prepare to enter the labyrinth is whether to walk or not.
David Tolzmann, Chief Geometer and Labyrinth Builder