If you are looking for the Alps' real deal - then you have to come to Tyrol. It may be true that the Western part of the Alps has peaks slightly higher than the mountains of Tyrol - though when you're looking at them from the ground you wouldn't know this. It certainly has to do with the rugged shapes of the peaks of Tyrol - but mainly it is a matter of culture. In Tyrol you find that kind of people that all around the world is associated with the Alps: Mountain-men with a rough charm, proud of their traditions and superstitions, backward and open-minded at the same time, and with just the folklorist clothes that stand for the Alps, everywhere, from Japan, through the USA, to Moscow.
It also helps that Innsbruck is not only Tyrol's capital, but, one could say, the unofficial capital of the whole region of the Alps.
Tyrol has a population of 701 thousand, and it borders on three other countries: Germany, Switzerland, and Italy, as well as on the Austrian states of Salzburg and Vorarlberg. The capital Innsbruck is inhabited by 117 thousand people. Obviously, tourism is the major branch of Tyrol's economy, but you'd be surprised to see where else they are big: For example in IT. This is just one example of this unique blend of archaic tradition and ultra-modernism that is called Tyrol.