How safe is Vienna (and Austria) for tourists and to move around? Vienna is very safe; it is ranked as number 3 to 5 on the world safest country list (on various indexes). Tourist areas are generally safe, both for single tourists and groups or families, but extra caution for pickpocketers is advised. There are also people dressed in period clothes (Mozart, Beethoven) that will try to sell you tickets for concerts downtown that might be slightly overpriced (most of the tickets can be bought online).
Vienna and Austria in general have low to very low crime rates and from that area can be considered very safe.
As far as weather and natural disasters are concerned, there is a danger of flooding in the area along the Danube river as there was a large flood several years ago. There is a notification system in place and if you happen to be in the area in case of torrential rains that cause flooding, you should be vigilant.
One thing that you should be paying attention as a visitor in Vienna is your walking path, meaning to follow pedestrian routes and not walk on bicycle tracks. They are marked very well (mostly), but they are crossing and overlapping each other, especially near pedestrian crossings and you might be on the way of people on bicycles and scooters. Many of them drive very fast and accidents can happen.
Safe travels and see you soon!