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> Maybe if you are lifting the entire city.

This would be a really cool element in a sci-fi world

A long time ago I did the napkin math to check if it'd be worth it to lift a skyscraper up and down just slightly for energy storage. You know, you'd just use adjusting ramps as the height changed ever so slowly. Not surprisingly, it's surely not worth it. The empire state building could run some tea kettles, but, yeah, no.

Japanese TECOREP brand demolition system generates power as it lowers material down from skyscrapers

https://sipilpedia.com/tecorep-system-high-tech-demolition-s...

I calculate a rather better figure for the Empire State Building:

365000 tons × 9.81 m/s2 × 1 m = 1 MWh

which ought to at least be enough to provide short term backup power to the whole building.

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