Austria is a delightfully small country to traverse but the distances between important locations are still not inconsiderable, so I wouldn’t want to have one city as my base and keep returning to it. However, if you would rather stay in one place,Viennawould be my pick, partly because it’s where you are most likely to land (the capital is Austria’s most internationally connected airport, unless you are crossing over the Swiss border to Innsbruck), and there are plenty of connections to all the rest of the country.
I would suggest staying at all three places for a minimum of a couple of nights each, depending on your timetable. Frequent high-speedInterCity trains(there are comfortable buses, too) connect Vienna to Salzburg (2hr30min), Salzburg to Innsbruck (1hr50min), and Innsbruck to Vienna (4hr15min), a route I would favour. Graz and Villach form a triangle with Salzburg and are both 2hr and 30min from it. Tickets can be purchased easily, even without advance reservations.
Vacation rentals will suit your budget for accommodation in expensive Austria, and apartments usually come with well-equipped kitchens. You will find a range of options atflipkey.com/austria-vacation-rentalsandvrbo.com/vacation-rentals/europe/austriaalthough something central at under € 100 will be difficult to find.
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