Regardless of how you go about this, there will need to be a list of objects that you care about the distance from and every time the player moves, you have to iterate over that list and check the distances. You can have your own table of objects and an enterFrame listener (or have it tied to your move somehow) and loop over the objects, compute the distance using the Pythagorean theorem. physics.queryRegion() is likely going to do the same thing. It’s a matter of you doing the work or letting an API do the work for you.
Of course, you can always do some test cases and see if you’re own list management may be more efficient. Obviously, if you’re not using physics, using physics just to get to physics.queryRegion() doesn’t make sense.
Rob