There are several solutions to supply-demand matching and buffering which either do or should work.

A key is to think of this in terms of matching supply and demand rather than simply as storage. We've adapted over the course of a century or so to a regime of dispatchable supply energy, with little use of dispatchable demand. There's also been little consideration of major behavioural, social, economic, and land-use changes which will be prompted by changes to the energy regime. Much the same way as major impacts of internal combustion engines on land-use, construction, transport, and trade were almost wholly unanticipated, most discussion today is framed in terms of "how do we sustain present behaviours and activities under a novel energy regime" (if not quite so explicitly).
The short answer is: you don't.

Automobiles, rail, air transport, and powered shipping gave rise to suburban sprawl, transcontinental trade networks, same-day globe-spanning travel and light cargo, and transoceanic shipping centres, along with tremendous centralisation of activities in zones of maximum productivity (often, yes, through massive externalised costs). Little of those impacts was foreseen in the popular or academic literature of a century (or even half-century) ago.

There's much of economics that's badly broken, but a part that's useful is the notion that behaviours do change tremendously in the face of changes to real and expressed costs. The Jevons Paradox cuts both ways: increased efficiency increases total use, whilst increased costs will decrease total use of some resource or factor. (Increasing efficiency is equivalent to saying "decreasing cost".)

Addressing energy specifically:

Expect to see far more dispatchable load, effectively, "making hay whilst the sun shines". High-load, but bufferable uses such as thermal heating (water, space, thermal storage), electrically-driven refinement (aluminium smelting, electric arc furnaces), reverse osmosis desalination, and the like, can if not "store electricity", then cache useful activity whilst supplies are abundant. Smaller industrial, commercial, residential, and possibly transport loads may also see time-shifting on a similar basis.

For direct storage, pumped hydro, compressed air energy storage (CAES), grid-scale batteries (an area with frustratingly slow development, though some promise, especially with cheap-and-abundant if not highly-efficient electrolytes), are presently proven. There are a number of schemes which don't work particularly well -- flywheel storage doesn't seem useful for much besides replicating today's "spinning reserve", nor do supercapacitors look as if they'll offer much beyond grid-scale power conditioning.

Two areas which offer tremendous promise and fairly high probability of success are grid-scale thermal energy storage with regeneration and electrically-based fuel synthesis appear at least on a back-of-the-envelope basis to provide national-scale grid-level storage capacity good for weeks (thermal) to millennia (fuel synthesis). The round-trip efficiencies are not great, but the simplicity, safety, and in the case of fuel synthesis, exceedingly long-duration storage, transportability, and utility of the derived medium are huge advantages.

Thermal energy electrical storage is mostly used now in solar thermal generation plants, but could be utilised in other forms. Large insulated tanks of molten salt driving traditional steam turbine generation could offer weeks worth of grid storage for the US in a total storage capacity roughly of the magnitude of extant oil transport storage facilities in Oklahoma.

Synthetic fuel generation, first suggested for nuclear power at Brookhaven National Laboratory in the 1960s and researched for over 50 years at Brookhaven, M.I.T., and the US Naval Research Laboratory, has yet to be proven at national scale, but the basic chemistry works, it's similar to coal-to-oil processes used by South Africa and Germany since World War II, produces direct analogues to current fossil fuels (methane through bunker oil) but is carbon-neutral as the carbon itself is sourced from current biosphere reserves, principally seawater.

Otherwise: expect to see tremendous differences in how energy is used, in construction based around heating and cooling loads, lighting, transport, and other processes.