ARES (rail energy storage) builds a rail-line uphill, for example. Rail cannot handle a very steep slope, but a gentle hill climb will build up potential energy fine.
In the case of vertical-based gravity storage, I'd imagine that lifting blocks to the top of a cliff (or down a valley) would be most efficient.
I mean, Pumped Hydro is gravity storage, and does just that. Pumping water up a mountain and generating energy by dropping it back down. But presumably, we don't want to use water in the Western states (where water is scarce). So Gravity-energy storage WITHOUT water is the goal.