These places are NOT Kosher establishments. You may order from them only known Kosher brands.
A for Athens rooftop
Very centrally located in Monastiraki Square, this is a very popular place both with Athenians and tourists and can get crowded. It has a stunning view of the Acropolis and Monastiraki Square below. You can call to make a reservation to secure a spot (only for the evenings after 19:00).
Info: entrance is from Miouli 2-4 St. 2103244244 http://aforathens.com/index.php/pages/page/top-floor
Right off Monastiraki and also with a great view. The first floor is for food, the second floor functions as a bar with louder music, and third is the rooftop with great 360 degrees view on the city, and of course the acropolis.
Info: Entrance is from Ifaistos street, 2 right off Monastiraki Square, 210321 0006. https://www.facebook.com/threesixtycocktailbar#!/threesixtycocktailbar
Galaxy Hilton Athens
The top floor of the Hilton Athens has a great view of the Acropolis and Lycabettus Hill. It is chic and trendy, with nice cocktails, although not cheap.
Info: 46 Vassilissis Sofias Avenue, metro Evangelismos (red line).