Yes, other cities would have some mechanism of free grain distribution, and not only major ones. For example, this is an image from Pompeii of a candidate for office (note his white toga--the toga candidus) distributing bread. We also have epigraphic information from Asia Minor and papyrological information from Egypt of regular grain distribution, so we can say with some certainty that this was a common form of political activity.

However, distribution is only half the story, because Rome's grain dole combined the distribution of grain the citizens with the acquisition of grain from the provinces through tariff incentives and outright tribute extraction. And indeed we do see evidence of grain acquisition from other major cities such as Carthage and (later) Constantinople. Undoubtedly it did not command the sort of sheer scale that the Roman dole did, nor could it use the same coercive force, but it does show that other cities were facing problems similar to Rome's and using similar solutions.

A difficult aspect of the Roman empire to remember is that while there was an imperial administration, there were also countless parallel local administrations. Local cities would have their own Senates (called curia), their own elected magistrates, their own citizenship rolls and even in some cases issue their own coinage. The problem of course is that virtually all our written evidence pertains to the imperial administration and mentions the local governments only in passing.