Do you mean [itex] \hat r [/itex]? It certainly does have a direction. It points radially outward from the spherical coordinate system origin. I'm still struggling to see where your confusion lies. Maybe it is this. In a Cartesian coordinate system the unit vectors point in the same direction everywhere. In a curvilinear coordinate system like spherical coordinates, the direction of the unit vectors varies from point to point, so the unit vector [itex] \hat r [/itex] points in different directions at different places. Could this be the point you are missing?