A great city to visit is Athens, Greece. The best thing you can do it is to stay at least three days and not only for the Acropolis and the wonderful museums, but for the little treasures that you can find in your long walks.
The best walk is around at Plaka in which you can see the quite face of the busy Athens with some wonderful coffee shops and all kind of restaurants and tavernas.
For the "alternative" travelers i would suggest Exarchia district were you can find some of the best and oldest bars with good rock and jazz music. There you can find some little theaters some wonderful tavernas and a lot street food.
It is worthy to come and visit Athens and discover the other side of it.
