If you want to visit Athen from Vienna in the most cheapest way i am going to tell you how you can do it. I spent 3 days in Athens and that costed me all together with the flight less than 80€.
Best way to travel to Athen from Vienna is to take flight from Bratislava. Bratislava is 80km away from Vienna and it is very good connected with Vienna. You have buses almost every 30 minutes and they costs usually around 7-8 €. There is a good train connection. You can even go with the boat. I got my ticket on discount (slovak lines) so my trip to Bratislava airport(Letisko) costed me only 1€ Trip takes around 1h till the Airport!
From Bratislava to Athen there is a Ryanair flight. You can find ticket for both ways for less than 50€. Letisko airport in Bratislava is a small but new and modern airport. It is very close to Bratislava and transport to the city is incredibly cheap. You can take city bus to the main train station for only 1.20€. Very cool!
Flight from Bratislava to Athen takes around 2h. Athen is in another time zone than Vienna and Bratislava so don’t forget to adjust your time. I had a nice weather during the flight but unfortunately i got a seat on the plane without a window so i didn’t enjoy the view very much.
Athen’s airport is much bigger than one in Bratislava so you will need some time to get out of there. I took metro to the city centar. It depards every 30 minutes and ticket costs 8€. It was a long ride till the centar. I think it took 40 minutes or something like that.
I hope I helped you with some of this informations and here are some photos from my trip to Athen.