We do have a ton of salt caverns actually, many centrally located (Hutchison, Ks if you’re interested. Great air and space museum there too oddly enough)

Unfortunately, water has the nasty habit of dissolving salt. As the Lake Peigneur Disaster taught us, mixing the two is generally a really bad idea.

That's how they create the salt caverns in fact: they pump hot water below impermeable limestone formations that were created when Kansas was an ocean 290 million years ago during the the Permian period. They use seismographs to watch the cavern formation and steerable drill bits to shape the formation.

Still need a place to keep all the water after you pump it out of the cave.

In theory, yes. But I do not believe an oil field would be suitable.

Hydro relies on a pressure difference. This means you want the turbine located at the lower reservoir, which is going to be tricky with an oil well. Oil fields are not a hole filled with oil but instead are just porous rock, which greatly limits the flow rate you can achieve from a single well. Oil fields are already pressurized, so you'd actually need to put in energy to get water in there.

And of course you'd be contaminating the water with oil and gas, which makes the upper reservoir a bit of an issue.

Sounds like oil fields are better suited to compressed gas storage. I wonder if salt caverns would work though? To solve the pump location issue, you could perhaps pump down air to get the water to come up.