This is an entirely subjective question.

I mean do we count knowledge from Socrates and Plato as contribution to society, and how much so? They are still being taught in schools today, from direct or translated texts.

Roman roads and aqueducts, made fresh water and long distance trade vastly more available to the common person.

Military might and order, can't be ignored either.

Democracy?

Music?

Mathematics?

To be honest the question is almost impractical to answer. And will entirely depend on what a particular person feels is more important. And so, for real historians, which I am not, it depends on what you mean. Music in it self probably didn't add a whole lot to people's lives on a day to day basis, but a lot of Music theory is directly based upon Pythagoras' original major scale (which did change and would be an entirely different topic), and without that we would be hundreds of years behind. But was that the most important addition to society? I don't know, I do know that it did add to it though.

Rome and Greece had time of war and gained massive amount of land which allowed a lot of invocation to take place and spread beyond it's original borders, they would "take" it and bring it back to Rome. That process was probably overwhelmingly beneficial to how we see those historic cultures.

When Rome fell, a fair amount of information and technology was lost to most of the people of the world, per se, only to reemerge later from old texts, to a greater or lessor extent. Was it then really Rome that did that or people later that now could use the information and propagate it much further than Rome ever did.

But if I were to answer, the most important addition to society that Rome and The Greeks added, was probably the ability to have all of these advances to be possible, to have it be a place that rewarded Plato for being a philosopher, that rewarded great architects for building great thing, great artists to paint/sculpt/ perform great works, for rewarding military leader for their prowess, that rewarded its people for advancing society, and creating a society that was able to have so many advances thrive in way that wasn't possible before. An appreciation for things that were not before. That's not exactly a thing in the classic sense, and certainly wasn't always the case in everything, and certainly wasn't always done for purely intellectual reasons.

And we have to remember particularly with the Greeks that they didn't necessarily see themselves as Greek, but Athenians or what have you. We group them together, for good reason yes, but it's not entirely accurate.