Budget - up to 100 euros.
Athens has a rich history, so that the cultural program can be too intense.
We advise you to take a city tour to see all the main attractions. They are: the Acropolis, and the Theatre of Dionysus, and the Agora marketplace, and the mountain of Athens, and the Temple of Zeus and the stadium Panathinaikos and much, much more.
You can enjoy the waterfront on the Athenian Riviera, it's only in 40 minutes from the city center.
Of course, Athens is famous of its shopping tours (then you definitely need more than 100 euros per day :)). Good luck!