Where are the magnetic fields strongest near a bar magnet?

Near the poles.

Consider a bar magnet. Magnetic field lines around it starts from pole N, and terminates at pole S. Thus, following situation occurs: Field intensity is directly proportional to line denseness. Thus, Magnetic field is stronger near the poles.

If you move perpendicularly to magnet axis, starting from its middle, you will meet with field lines more rarely. But if you move around poles, you will more frequently crash with field lines.