Compressed looks a good solution, and you could probably replace the electric generators by compressors directly at the turbine shaft, though the pressure required to store a lot of energy sounds a bit frightening.

Unfortunately there are some "Laws of Thermodynamics" that say that compressed gas is a rather inefficient way of storing and recovering energy. Efficiency (thermodynamic) is usually better using larger volume at lower pressure, but the volumes required for "city scale" storage, at reasonable effectiveness, are immense. The volumes that can be accommodated for a vehicle, or even a single-house, dictate rather high pressures to obtain useful energy density. "Compression losses" followed by "expansion losses" make this a poor scheme in most situations.

Compressed nitrogen bottles are used for "emergency actuators" in many places, particularly in large aircraft. You can pack lots of energy into a small and relatively lightweight package; but the energy consumed to pack it is about 3 times what's contained, and the energy that is recovered (usable) when you fire the release is about one-quarter of what was "in the bottle." (From one specific, but pretty typical, design I'm somewhat familiar with.) Less "explosive" compression and recovery would do a bit better, perhaps.

A few moderate sized facilities have used "air bladder" type storage, where the energy is stored by moderate compression of air (sometimes another gas) contained in a sealed container, but the compression is done by pumping an "incompressible" fluid, often water, in and out. The thermodynamic losses are somewhat smaller for pumping liquids than for gases - usually. On a small scale, this method is used for many home well systems, with the pump putting "stored pressure" into a small reservoir, and the air pressure providing the "pumping work" to deliver the water to the tap as needed, avoiding the necessity of having the pump turn on everytime you draw a cup'a.

Larger ones may occupy an acre or so of ground, with dead-weight(often concrete) "roofs" to contain the pressure, and are used in a few places in lieu of a "water tower" to provide municipal water supply pressure, or for pumping the crud in sewage treatment processes.

John