In fact, it’s so far east that the Vienna city limits are only about 30 km (17 miles) from the border with Slovakia. It’s further east than the capitals of the Czech Republic (Prague) and Croatia (Zagreb), and almost as far from Austria’s western border as Paris is.
Vienna’s position in “Austria” is fairly new: the country we recognize today was only established in 1919. Vienna was previously at the head of the huge Austro-Hungarian Empire that stretched much further north, east and south. The city was actually in the western part of that empire – it’s the red dot on this map:
So the location (and size) is a historical anomaly.
One advantage of this location is that it’s only a short drive to Slovakia, the Czech Republic and Hungary and it takes no more than 3-4 hours to reach their respective capitals (Bratislava, Prague and Budapest).
Although Vienna is not in the Alps, the mountains are not far away, either. The first proper ski resorts are around an hour’s drive away to the southwest, and the alpine foothills are even closer!