We rode the reverse direction to you, Prague to Budapest, Aug 27- Sept. 18, 2005. Actual riding days were 16 for the whole trip, and 1,111 kilometers. Nine riding days for us from Prague to Vienna, which seems to interest you most. Since we weren't in a hurry, we detoured to see quite a few sites. Our nights were at: Sedlec-Prcice, Hluboka (in the wonderful castle!), Cesky Krumlov, Trebon, Telc (the "candybox towns"), Slavonice, Hnanice, Valtice, Vienna.
The Danube route didn't interest us since we had ridden it some years ago, but it is lovely - more German than Czech in flavor though. The Czech bike route system is amazing! Signs on all the routes, good arrows, wonderful smooth and nearly car-less roads. I had a hard time getting these bike route maps from the US (ordered from England, I believe, but don't have that info in front of me), but perhaps in Budapest they'll be easier to come by.
We found the riding much more pleasant in the Czech Republic than in Hungary (fewer roads, so bike routes followed busy truck routes), though the countries were both fascinating. We also used the bikeline Donauradweg book in Hungary.
Can't imagine that you would get to see too much doing Vienna to Prague in 3 days - perhaps better to choose some part of the route with sights that interest you, and do the rest by boat or train?
Also, the Greenways route mentioned by someone else is probably not the best one for you if you want to make good time! We had their route booklet and I spent a lot of time on their web site, but we rarely followed their route. Much of it on field tracks and remote dirt paths... we wanted to see the villages. (Which amazingly all looked like they had been painted by a Disney crew the week before! )
Sorry to be so wordy - this was one of my favorite trips ever! Hope to get back to the Czech Republic to cycle again.