Answer
There is no point of zero net electric field anywhere off the axis.
Work Step by Step
We can write the general equation for the magnitude of an electric field:
$E = \frac{\vert q \vert}{4\pi ~\epsilon_0~r^2}$
Note that an electric field points toward a negative charge and away from a positive charge.
In order for the net electric field to be zero, the electric field due to the $+q$ charge and the electric field due to the $-3q$ charge must point in exactly opposite directions.
At any point off the axis, these two electric fields will not point in exactly opposite directions since an electric field points toward a negative charge and away from a positive charge.
Therefore, there is no point of zero net electric field anywhere off the axis.
