I have drawn the magnetic field of Levitron. The picture schematically shows a magnetic field around Levitron. The lower four spots (two of white and two of black) are originated by the plate. The upper two spots are originated by the top (you can not see these spots in some pictures, since the spots are overlapped with those of the plate.)
You could imagine the magnetic field by
H = rot Athus, the lines in the picture correspond to the magnetic fields. Attractive forces are existing between the same color spots. Repulsion forces, between the different color spots. The pictures are the cross sections. Therefore, the shape of vector potential is a circle as a top view. In the cross sections, white color means coming direction of the vector potential and the black color means the opposite direction of it. The denser contours represent the stronger repulsion (attractive) force between the different (same) color spots. The color represents the direction of the vector potential. To see the vector potential, just imagine the rotation of the picture by the axis of the rotation located at the center line.
Each picture shows the magnetic field for the different hight of the top. You can not see the vector potential for the magnet-top which is overlapped with the field of the plate in the first picture. The later pictures show distinguishable spots between the magnet-top and the magnet-plate.