As you have stated that you are from a EU or EEA country (or Switzerland) and your lenght of stay is shorter than 3 months, you don't need a visa to enter Austria and you enjoy freedom of domicile.
The only thing you need is a valid travel document (passport) or identity card.
However, what you need to do is to register at the registry office. (Meldeamt)
When: Within the first 3 days of arrival
Where: At registry office --> See "Links" for registration offices in Vienna. You can register at any of the listed registration offices. It does not need to be in the same district you are going to live.
Things to bring:
In case you stay at a hotel/hostel, the reception will register you so you don't need to go to the registry office. However, as soon as you move to a private place you have to register within the first 3 days.
Please note: FeelsLikeHome is not legally in the position to give any immigration advice on applying for visa! The information given is collected by to the best of knowledge but we don't take any guarantee for them and assume no liability or responsibility. Please confirm the information given with the Austrian Consulate i.e. the embassy that serves your region.
We try our best to provide correct and up-do-date information. In case you come across a mistake or a change in law - please inform us so we can update the information given. (firstname.lastname@example.org)
Your FeelsLikeHome Team!