In the Vienna Central Train Station (Wien Hauptbahnhof) to catch the train to Salzburg (2.5 hours trip) and spend a day there in Untersberg, Mönchsberg, the old city of Salzburg and the famous Getreidengasse. Then take the night train to Munich and then Heidelberg to visit a friend for 3 days, the historic city of Heidelberg, as well as Weinheim and other beautiful places in its surroundings…before heading south to Freiburg im Breigsau (2h trip) and finally Zurich (1h 45min trip) for the weekend. Finally take the Monday morning train to Vienna, along the Zurich lake, between the Swiss Alps and then through the famous Albergline (one of the most scenic train trips in Europe) in the Austrian Alps from Bludenz to Innsbruck. That is expected to be an amazing one week trip, which you can do at very low cost!!
Breakdown of costs with everything booked only 2-3 days in advance (might cost a bit less if you book well in advance):
Train tickets 122 Euros: Vienna to Salzburg 24 Euros, Salzburg to Heidelberg 19 Euros, Heidelberg to Freiburg im Breigsau 20 Euros, Freiburg im Breigsau to Zurich 20 Euros, Zurich to Vienna 39 Euros.
Accommodation in Zurich 70 Euros (2 nights, sharing an apartment with my friend on the Carnaval weekend, cheaper if you go in the week).
Transportation within the cities and to the outskirts, including cable cars up to the mountains and entries in museums cost 100 Euros max.
I have estimated a further 200 Euros for food and drinks in some of the most beautiful bars and cafes of the cities, not much more than what I would need to feed myself for a week in my hometown.