Calculating location with 4 piezo's
You might want to look into how LORAN works, as I believe you can do something similar.

First premise: You want to look for the initial transient caused by the impact propagating to sensors in various places on the periphery.  The signal in the material will end up bouncing around quite a bit before it dies out, but the leading edge of the initial transient should be unambiguous, so use that.

Second premise: You have no idea when the ball actually hits - you can also measure the difference in timing between when various sensors first detect it.

So take any two sensors, measure the time lag between when they detect the ball, and convert that via the speed of sound in your material.  This yields the difference in the distance of the impact point from the two sensors.  If you know the position of the two sensors, and plot the curves of points which satisfy the equation of the measured difference in distance from each of them you can a class of conic section called a hyperbola.  

But so far you do not have an answer, but only a pair of curves along which the impact must lie.  So now take at least one new sensor, and repeate the exercise generation a new equation.

Combine the equations and solve to find the intersection of the curves - this is your point of impact.  It is possible to have more than one mathematical solution, but I think you will find that only one possible solution lies in the area between the sensors.

(Unfortunately, the ATmega328p A/D converter probably isn't fast enough to do a good job of this - at 10KSPS each sample is around 34mm in air, and around half a meter in typical solids - so you either need a much faster A/D, or else tune a comparator circuit to detect pulses and measure them with ATmega timer channels.)