Do not stay at the airport!
Since there is the new Train to the city, take the chance!
It leaves the airport every 30 Minutes and takes only 16 Minutes!
It costs 9 EUR one Trip.
It takes you to the new Station "Wien Mitte" Where you have good connections to the U-Bahn or Tram.
Tiemetable and Infos on:
http://www.cityairporttrain.at/
On the way back you can check in at the city-air Terminal in the City Center!
If you have not been to VIE you should definitly visit the Stefansdom
(Two Stops U3 dir. Ottakring)
and have a cup of coffe in the SACHER!
If you mind shopping, the "Kärntnerstraße" (Leavign form the Stefansdom) might be a good adress!
You find a map on
http://www.cityairporttrain.at/wieninfo/wienplan/
Vienna is a much too nice town to waste the time at the airport!
The AUA Lounges are much better than LH Lounges on other airports, but they are not nice enough to spend 7 hours!!
Have a nice time in one of the nicest towns in Mid-Europe!
Alex