East and West
The magnetic north pole of a compass needle always points towards Earth's geographic North. This direction is the magnetic south pole of earth's magnet. Remember opposite magnetic poles attract.
We also know that lines of magnetic field of a magnet start from its north pole and end at its south pole.
When a bar magnet is placed in north-south direction with its north pole (magnetic) pointing towards earth's north (geographical) pole the combined magnetic field will look like as in the figure below
The Neutral Points, where the combined magnetic field is zero will lie on the east and west sides of the magnet as shown by mark
Notice the direction of both magnetic fields.
Magnetic fields in the NS direction add to each-other being in the same direction.
Whereas in the EW direction, at some points the magnetic field due to bar magnet and the horizontal component of the earth’s magnetic field are equal and opposite to each other. The resultant magnetic field is zero.