Possible layover day in Vienna - Customs question

Why not spend the night in Vienna and take a train the next day to Budapest?

If that is not feasible, you would be able to see a few things with a long layover. If your flight arrives at 9:25, you will be out of the airport in about an hour - let's say 10:30. When you say customs above, what you really mean is immigration and, yes, you will need to go through it. Customs is just an area you walk through and stop only if you have something to declare. So when you are out, I suggest that you take a taxi to maximize your time. The S7 and CAT are train options, but will eat into your time. Have the taxi driver drop you off at the Opera House. Walk up Kaerntnerstrasse and visit the Cathedral. Have lunch at Figlmuller's. Walk down the Graben, turn left on Kohlmarkt and then turn right on Herrengasse. Go to Cafe Central for cake and coffee. Back track on Herrengasse back towards the Opera House and get a taxi back to the airport. You'll need to be heading back around 3:30. You won't need to go through immigration again as you will have already entered the Schengen zone (EU membership is not the same as the Schengen).

Thanks for the insight. Staying overnight is not an option, as it turns out. This gives me one more exciting part of my trip to look forward to.

I'm sure you'll enjoy your visit, though short.

I looked at Rick's highlights and removed those which do not interest me as much. How much of this can be done in 6 hours? I realize that I cannot do everything, so efficient logistics are key. The palace, listed on the bottom, looks awesome, but if it is far away from everything else, it could limit flexibility.

▲▲▲ Opera Dazzling, world-famous opera house.
▲▲▲ St. Stephen's Cathedral Enormous, historic Gothic cathedral in the center of Vienna.
▲▲▲ Hofburg Imperial Apartments Lavish main residence of the Habsburgs.
▲▲▲ Hofburg Treasury The Habsburgs' collection of jewels, crowns, and other valuables — the best on the Continent.
▲▲▲ Schönbrunn Palace Spectacular summer residence of the Habsburgs, rivaling the grandeur of Versailles.

By the time you get off the plane and clear passport control then make it into the city it will be 11am at best. Take a cab straight to the Opera House. From there walk up the Kärntner Straße to St Stephen’s. Stop and eat lunch, if the weather is good you can sit outside. Get a guide book for all of the sights along this pedestrian road and up a few of the side streets. Lots of shops too. With lunch you can easily spend 4 hours. 4hrs plus 11am = 3pm + 30 minutes back to the airport = 3:30pm plus 1.5 hours prior to flight time yields 5pm. That leaves you with a 20 minute safety factor. Or, “miss” your connection and take the train for about 29 euro and be in Budapest by 2pm. Of course your luggage might be impounded in Vienna and then detonated just to be sure its safe.