Vienna already is a pretty bike-friendly city. And still, politicians are working on improving the network of bike lanes covering the most important routes.
I definitely recommend everybody to try and discover at least some parts of Vienna by bike. The first district is not a good idea, as most of it is paved with cobble stones, but all the surrounding districts are great to bike through. Also, visiting Prater park is way easier by bike than on foot. The same applies to Donaukanal and Donauinsel, and everything in those areas, like Friedhof der Namenlosen (no english wiki page?!). I still can’t believe how fast one can go somewhere compared to public transport and of course walking. It’s all about the first step!
If you’re not from Vienna, check out Citybike Vienna, a nearly free way of renting bikes in the central areas of Vienna.
I’ve even gone so far as not to renew my annual ticket with the public transport :)