[0ldskool]

Pumped storage is simply a gravity battery. There are vertical gravity batteries that can be built anywhere. Basically they are giant cranes that lift heavy blocks high up. This is the storage component and requires electricity. When we need to drain electricity they move the high blocks to a lower elevation using the crane. This generates electricity. This seems like the perfect type of battery to me for urban cities with large towers already.

[xyzzyz]

The sort of battery you describe is utterly non-viable. The amount of energy you can store with solid blocks is extremely small relative to the cost of the structure. Do the math. With 100 tons weight and 100 meters lift (an enormous structure) you get something like 1 (one) dollar worth of electricity, which is bupkis.

Pumped storage works, because it pumps absolutely enormous amounts of water. You can't handle comparable amounts of solid blocks similarly easily.