This answers the "how", but not the "where". Since energy itself has mass, we would expect the potential energy to carry mass as well; and that that mass/energy should be concentrated in some region of space.
Potential energy is a property of a system rather than an actual physical thing. It's not energy an object has, it's energy an object potentially has relatively speaking. And it's relative to whatever you use as your reference point in your system.
>Since energy itself has mass
Energy doesn't have mass. It is equivalent to mass.
The answer to the question of 'where' is the underlying (non-gravitational) physical field (and in particular the electromagnetic field, which is long-range, whereas the nuclear fields normally get folded into mass terms). The case of gravitational potential energy is a bit more subtle: It's excluded from the stress-energy-momentum source term of the Einstein equations, and there's no expression for a gravitational stress tensor (though there are pseudo-tensorial approaches).