[Suicide Junkie]

Why would you think gravitational potential energy is not real?
You drop a bowling ball, and it crushes your toe. That's definitely real energy.

On the small scale, it simplifies to mgh. For larger scales you need integrals. But it is all very straightforward.

The only difference is scale. In the spring, you have electric forces pushing or pulling (but you have to look on the molecular scale). Gravity works on scales big enough to see and just pulls.

BTW, since gravity is always attractive, the arbitrary zero point is generally placed at infinity. So if you fall inwards, your gravitational potential becomes negative.
Conveniently, setting the point there means that if your total energy is positive, you can escape. If the total is negative, you're stuck in the gravity well unless you steal some energy from something else.