Karlsplatz is one of the best-connected public transport hubs in Vienna. Is there provision for leaving a bicycle securely there whilst I travel for the day on public transport (U-Bahn, tram, etc) and then return in the evening? I might be doing this regularly.
There is no Google Street View for Karlsplatz, so we can't use it to find bikes parking (it's not a very comprehensive method of finding bike parking, anyway)
Instead, I found this: https://www.wien.gv.at/verkehr/radfahren/stadtplan.html
If you go to the second section, labeled "Radabstellanlagen", you will see a map that lists all kinds of bike facilities around the city including bike racks.
Finally, here are more tips about parking a bike safely: http://www.argus.or.at/info/rad-und-abstellanlagen/fahrradabstellanlagen-wichtiges-element-radverkehrsfoerderung