Your question raises many issues, so let's try to identify them and clarify some points.

1. Classical Athens as a cultural centre

Athens was during the 5th and 4th century BC at the top between the Greek poleis both in power and prestige; as a cultural centre it attracted many thinkers, artists and such from abroad, so that many non-Athenian Greeks contributed to Athens' fame and intellectual growth; Aristoteles is maybe the most famous exemple, but also Lysias, Protagoras, Diogenes etc. were metics (μέτοικοι = resident aliens).

So not all intellectuals in Athens were Athenians; Also, not all Athenians were intellectuals. I would not say culture was a few aristocrats' business: after all any free male went to the theatre and such. But surely the leisure class had the big share in the cultural production of the time. Add to that that you have to count out most slaves and women, who were no little part of the population!

Furthermore, we are talking about people living in a very broad period, and many people are as chronologically far to each other as we are to Victorian era. Sure, the literary, artistic and in general intellectual production was great, but let's not think of Athenians spending their lives in philosophy and art.

As for the quality, consider that what we have of Antiquity is the result of two millennia of selection and canonization; in other words, only the best survived, giving us the false impression that all Athens produced was prime quality. Think about drama: each year at Athens 3 dramatists with 3 tragedies each were competing at the Theatre of Dionysus. Between, say, 480 and 380 it's 900 works. Of this massive production we have 32 works from just 3 authors.

I can't give precise percentages, but let's take the end of the 5th century. The estimate population (Gomme 1931, referring to 431 BC; outdated but it gives the order of magnitude) is circa:

TOT	300,000
slaves	100,000
metics	30,000
Athenians	170,000

Of the Athenians, the majority would be women and children (some 120,000) leaving at most 50,000 free citizens.

Of these several tens of thousands of Athenians of the late 5th century we know some thousands of mere names (less than 10%), and hardly a hundred of 'thinkers' (less than 1%) we can read and/or appreciate the genius.

2. Contemporary cultural life. Conversely, the supposed lack of intellectual value of contemporary US is not as clear as it may seem looking at us procrastinating on the internet. Quantitatively speaking, the cultural production of, say, New York, or London, in the last century is surely more abundant than Classical Athens: more people, longer lifespan, better education etc. We are inside this time and cannot see the whole polished picture as we can with Athens.

Lastly, if we have to engage in a new-style "Querelle des anciens et des modernes" it would be fair to compare the best of classical Athens with the best of our time (and I don't think today's cultural elite spends much time with cat videos).

As for the abundance of information we can grasp thanks to technology, I don't think that it's really determinant. Sure, it's easy to think of the ancient as wise men who used well their time creating important stuff while we spoiled brats waste time fiddling with toys, but that's the classical laudatio temporis acti "praise of the past time", something the Ancients already did, considering their time decadent in comparison with their strong forerunners. I agree that we have a flood of data noone before us could even imagine, and that we could make a better use of it, but a) it's not the only ingredient to produce something intellectually valuable; b) it's not that "data miracle" as commonly thought: having a lot of information means it's difficult to find the useful one.

We have lastly to remember that the average American is no doubt more literate and educated than the average ancient Greek. We look at the peaks of wisdom of a Socrates or of a Pheidias, but overlook the deep valleys of the common man.