I think Innsbruck is the closest, but Salzburg can't be too far also.
Geneva is 30 min dive to chamonix Mont Blanc
I've never managed Geneva to Chamonix in less than an hour on the Autoroute Blanche. My parents have an apartment opposite the train station car park in Argentiere, so that's a further 20 minutes. You've got to be doing some speed to do Geneva to Chamonix in 30 minutes!
However I still think Innsbruck is still the closest airport to Alpbach, which I think was the question