Yes, electric potential can be zero at a point even when the electric field is not zero at that point. ... At the midpoint of the charges of the electric dipole, the electric field due to the charges is non zero, but the electric potential is zero.

Where is electrostatic potential zero?

The electric potential from a single charge is defined to be zero an infinite distance from the charge, and the electric potential associated with two charges is also defined to be zero when the charges are infinitely far apart.

Is there ever a point where the potential will be zero?

What zero potential means, roughly, is that the charges in your system have cancelled out. For example exactly half way (or otherwise equidistant from them) between two equal and oppositely charged point charges, potential is zero.