Don't come in summer. December through February daytime temperatures regularly hit 45°C and the dust storms are serious; even locals largely stop moving in the middle of the day. The reason the town lives underground is that summer above ground is, plainly, unliveable.
The good months are May through September. Days are warm (low 20s°C) and nights cool, sometimes cold. July and August are the peak season for visitors, when the southerners drive north to escape their own winter. Roads to the Breakaways are reliably open in this period. Spring (October) and autumn (April) work too, with the risk of a few hot afternoons.