If you fly into Vienna's airport and are staying centrally then forget taxis and walk straight on to the CAT (City-Airport Train) not forgetting to buy a 16 Euro return ticket valid for a month.
The CAT whisks you without stopping, in just 16 minutes to the centre of Vienna. From plane to CAT is just 400 yards and from CAT to Vienna Hilton just 200 yards. So convenient!
Having trekked about 400 miles around Heathrow it shows you why more, smaller airports are the answer rather than bigger airports that you can't get to because of congestion.
There are some luggage lockers at Wien Mitte / City Airport Terminal but not as many as you'd think. They're near the McDonalds. Don't rely on being able to deposit your luggage as they might all be occupied.
Wien Mitte station
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