Hi Hendrik,
Generally Vienna is pretty good for bikes, in central Vienna there are a lot of bike pathways apart from the roads and in the outer districts in not uncommon to see People cycling alongside cars on the road. So you wouldnt stick out like a sore thumb.
The only thing id say as Ilja, some districts might be a bit hilly but thats up to you if thats an issue and if it is a heavy winter then I probably wouldn't cycle as it can get very snowy/slushy.
All that said I should probably also mention that Vienna has an excellent public Transport System and the monthly/yearly tickets are amongst the cheapest i've found in Europe- so thats always an alternative