Avoid driving while in Vienna. The streets are crowded, are usually one-way, and so can be quite frustrating for visitors. Parking is pretty expensive as well. Pedestrians have the right of way, so if you do drive, do so very cautiously.
The speed limit inside the city is usually 50kph, and 100kph on major roads, but is reduced to 30kph near hospitals and residential districts, and on highways it is a maximum of 130kph.
Austrian drivers are known to be not really polite on the road, so it's better to stay out of arguments while driving, and to take care of the right of way for all kinds of vehicles.
Passengers need not worry, since most taxi drivers take the fastest and shortest route whenever possible.