You would indeed have to pay to park. You can purchase parking "passes" in any traffik/tabak shop. They are usually pads with designated times for parking that you leave on your dashboard after parking your vehicle.
They are on the outskirts of Vienna and you can easily change from your car to public transportation (such as underground, streetcar or bus and tram) and the most importan its inexpensive too.
PARKING COST ONLY 3 EUR PER 24 HOURS.
There are many - very expensive - garages in Vienna's center (cost between EUR 30,- and 40,- per 24 hours, 3,80 - 4,- per hour)
An alternative are the "Park and Ride"-garages in Viennas suburbs, connected by Underground, bus or tram. The rates are about EUR 3,00 - /24 hours !
There is one convenient for tourists coming from north / east in
Erdberg,at the U3-station. It is close to the highway A23 and E60, see map at
An overview is given at http://www.wien.info/article.asp?IDArticle=3305
where you can find also P&R-garages for the western and southern city-limits
Good Luck !
Where to park your car if you arrive in this city ? Not easy.
There are many underground parkings garages. Some tips here :The Staatsoper Garage on Karntner StrasseIn front of the Museumsquartier, quite centralMultistorey carparks at Sudbahnhof & WestbahnhofInnere Stadt's area is a short-term parking zone. It means you can only park your car for 1 & a half hours ONLY. From 9 am to 7 pm, Monday to Friday onlyNEVERTHELESS, there's no parking restriction outside these hours !
The old city of Vienna and the surrounding districts (number 1 to 9 and 20) are 'pay & display short-stay-parking-zones'. When you park here you need a valid parking permit (to be bought in a 'Tabak Trafik' - tobacco store and at hotels) behind your windscreen from the first minute of your stay. The signs indicating the short stay parking zones are only posted where you enter these districts (it also happened to me that I got a ticket because I didn't know that!). I recommend you to leave the car somewhere out of the inner city and use the efficient public transport system! 30 min are 0.4 Euro. Fines are 21 Euro. 10 min are for free but you have to fill out a special permit for it!