"I just also think that it ended the development of Hellenic culture, since there were no longer city-states to fight for prestige by housing great thinkers."
I disagree - You had competition from Bactria, the Ptolemaic kingdom, Attalid, the Antigonid. Cities like Pergamum, Alexandria, Damascus, Antioch, etc, all flourishing. I mean Alexandria alone negates the view that Greek cities were no longer capable of producing great cultural achievement.
As for housing great thinkers and schools - you had Diogenes and his Stoics; the Skeptic and Epicurean schools. I think Greek culture was developing quite progressively. Indeed, it was this hotbed of ideas that was able to produce Christianity (which I think is a blend of Stoic & Cynic philosophy, mostly Stoic). You had Euclid, Eratosthenes, Herophilos, etc.
"they did not only translate Greek texts, they did not repress Greek ideas and they did build off of them."
How can this be said. Look at the case of Avarroes, one of the philosophers that the Islamic Golden Age people like to hold up as the exemplar of Islamic achievement? He was banished and his works were burned. He had no school. Most of the examples of 'great Muslim scholars' were non-Muslims who lived in Muslim lands. For example, Constantine of Carthage, who translated Greek medical texts into Arabic & Latin. Or Moses Maimonides, also not a Muslim. And most of what was done was transmission of work from other civilizations to the West, not original contribution. But the Muslims get the credit nonetheless, for example in their transmission of Hindu numerals. Other work was of a speculative nature than the Muslim rulers never bothered to apply.
Considering their supremacy on the world-stage for a good 4 or so centuries, and their inheritance of all of this vast knowledge from the Hindu and Greek civilizations, it is remarkable how little that was new was produced.