Are you asking about after the Hellenistic states themselves fell? Alexander's empire didn't collapse so much as it was divided into smaller states headed by Greek generals and their dynasties: Egypt under the Ptolemies, Syria/Iran under the Seleucids, etc. During their rule, what we call the Hellenistic period, Greek culture was heavily promoted and ethnic Greeks, in many cities, were the elite. I wouldn't exactly call a group of Greeks living in 200 BC Antioch an "ethnic community" when the Greeks were culturally and politically dominant.

The classic example is the Greco-Bactrians, who ruled briefly (in the grand scheme of things) the far eastern portion of Alexander's empire. This in turn spawned the somewhat longer lasting Indo-Greek Kingdom. Both of these, like their Eastern cousins, would have involved a Greek aristocracy and small urban centres ruling over a large population of non-Greeks. The 'legacy' of such a relationship is thus mostly going to be on government, administration, and architecture. So, for example, while these two Kingdoms only lasted until the 2nd century BCE and 1st century AD respectively, their legacy was a bit longer lasting. Once the leadership was replaced, the total population of Greeks would not have lasted very long and likely been assimilated into existing structures or displaced entirely (think the transition from Saxon to Norman in post-Conquest England).

So, what are some of those lasting legacies? One is the alphabet, which spread in Central Asia to a degree. The other was coins, and rulers of states in successor areas copied Greek patterns and merged them with existing ones to form a sythesis of Greek traditions with their own. By far the longest lasting influence has been on art and architechture though. Look at this statue from the 3rd century for example: http://upload.wikimedia.org/wikipedia/commons/8/82/PharroAndArdoxsho.jpg

Although it depicts a Buddhist subject, stylistically it could easily fit in with Roman and Greek statuary. Architecture also experienced profound influences, with the evolution of the Stupa being clearly influenced by Greek arts, a legacy that carries forward today.

However, there is not much evidence of the remnants of the actual Greek leadership of these communities surviving intact other than these cultural transfers. Evidence from later periods and more well attested areas, such as the Parthian empire, suggest that Greeks remained in their own communities when tolerated. For the Parthians, this meant that Seleucia, the first capital of the Seleucid Empire, was left intact and a new capital, Ctesiphon, was built nearby when the Parthians took over the area. The Greek city survived until sacked and burned repeatedly by the Romans during the 2nd century AD, and then the old Greek city was replaced by a new one with no clear link besides location to the old. So, in this example, we see what appears to be a cohesive and lasting Greek community for about three centuries or so, but a community extremely small and vulnerable. Given the turbulent nature of Bactria and Northern India politically, I suspect that the fate of the Greeks there was similar to that of the Greeks in Seleucia.