Until someone more knowledgable comes along, I can at least point to some anecdotal mentions of Greek city states that were known for their engineering skills, specifically engineering with regards to (naval) warfare, during Roman times.

Maybe the most famous is the Greek city state of Syracuse on Sicily. According to Diodorus Siculus, advancements in warships originated in Syracuse under the tyrant Dionysius. More than a century later, the famous philosopher Archimedes lived in Syracuse at the time Rome was at war with the city state. His contraptions are supposed to have helped protect the walls and the harbour during the long siege of the city.

Before the Punic Wars with Carthage, Rome was not known as a naval powerhouse. To be able to fight the Carthaginians at sea, they utilised the subjugated Greeks city states in the south of Italy to provide ships and sailors. The Greeks were of course known as a maritime people and had been travelling and fighting in the Mediterranean Sea for centuries. Greek cities like Neapolis and Tarentum that came under the Roman sphere of influence provided a good source of maritime knowhow and experience for the Romans.

Recently I was reading Strabo, a Greek geographer who lived in the Roman Empire. He mentions Massalia as known for its engineers for both ships and equipment for siege warfare. Massalia (modern-day Marseilles) was a western Greek city in the Gulf of Lion that had been allied to Rome since they were both just small city states. So throughout the centuries it's likely the Romans used the engineering services of their Massaliot allies for naval and siege warfare.

Although these examples are as far as I can comfortably go, I think it is important to mention that, in general, Rome used a lot of the knowledge and experience from the peoples they conquered. This is most evident with the Greeks, who contributed greatly to Roman intellectual and engineering developments. Famous thinkers during Roman times, such as Diodorus Siculus, Polybius, Plutarch, Ptolemy and many others, were actually Greeks. Even the Carthaginians, who the Romans completely wiped out, provided useful knowledge (most famously on agriculture).

A last mention should be that of course the Romans themselves, and especially the Roman legions, were expert engineers.