You are asking something very fundamental. The stored energy is a property of the whole system - the charged capacitor. I mean the metal, the insulation and the caused state change, the unnatural imbalance caused by charging. Of course it's possible to create a totally artificial border. We search the area between the plates where the electric field is substantially stronger than it was when the capacitor was not charged and say: "It's here".
But that's not the truth for everyone because that field gives to the electrons a possibility to drop and do some work. As well we could say "it's in electrons which are accumulated in the unbalanced way, we only calculate the amount of available work with the field".
In physics we have learned to keep the field existent, it's not only a handy concept to make calculations. But we still do not know what the field actually is. It's easy to us to understand that the invisible air around us is a bunch of randomly moving gas molecules, but we cannot say what the field is made of.
I would say it's just the field and it holds the energy that can be released by discharging the capacitor. It's a property of the space to have such state as electric field.
The energy in a cylindrical capacitor:
I guess you can think the capacitor as 2 concentric cylindrical capacitors in series - the inner one and the outer one. Imagine one cylindrical equipotential surface between the plates. Somewhere is the exact place for the border so that the inner capacitor has as much energy as the outer capacitor.
But if you think there's 2 intermediate cylindrical equipotential surfaces so that the capacitor is total three concentric capacitors in series there's infinitely possibilities to place the 2 intermediate surfaces so that the imagined capacitor between them contains half of the total stored energy.