This was a classic study abroad experience in many senses--you had some people who were there to party, others who were there to learn about the culture and history, and some who were somewhere in between.
We went to classes at the Athens Centre, a school which generally provides Greek language classes to travelers and new residents, but also hosts a couple of different study abroad programs. We got to have a traveling art history class with the resident archaeologist who had a very international upbringing and always had a good story to tell, whether about the art or about his life. He traveled with us on our field trips to Delphi, Crete, Aegina, everywhere. Our Greek language teacher was also fantastic, having developed most, if not all, of the materials from which she taught.
The housing provided is very close (within walking distance) to one of the locations of the traveling weekly market, and it was through my interactions there that I was able to measure for myself (outside of the tests in the classroom) how much Greek I was learning. There was one particular nice, older man that I remember who sold eggs. The first week I went to the market, all I could do was point, smile, and hold out a hand full of change for him to hopefully take the correct amount. The next week I was able to say "I want six eggs." The week after "I would like six eggs, please," and so on and so forth, until we were nearly having full conversations. He was so nice but also so insistent that I "spit" at him while pronouncing the words (to give it the correct vigor, I'm guessing) that it was easy to break down the bit of shyness I'd developed when trying out a new language. I may have eaten more eggs than I normally do during my three months in Athens, but the experiences that the language and cultural understanding brought about were priceless.
I was there in 2009, which is when some of the more recent economic woes were starting to develop, and there were occasions where you'd see heavily armed units on the streets because they'd been warned about rioting, and occasionally you'd see the rioting happen, although the Athens Centre did its best to warn us to keep away from certain areas if there was violence happening. I never felt unsafe, though, even when walking around on my own and traveling to more remote areas alone.