haven't read the responses yet (busy at work, will edit if i need to). but as i recall the prague-vienna greenway also covered roads to krakow and maybe budapest, yes? will you just be going from prague to vienna? if that's the case, I didn't take the route directly from prague to vienna, but the more roundabout path to krakow and budapest then vienna. here's my recommendation: DON'T DO THAT. prague to krakow is lovely. krakow to budapest can only be done through the tatras and many parts could only be done on the busy motorway. budapest to vienna was pretty boring - especially bratislava to vienna. i think that stretch was the single most boring day of cycling in six months.
however, all that aside to the best of my recollection the greenway in the czech republic and poland was very nice. I used a trek 520 with 35mm tires, so I was able to handle the few areas of gravel. i did the whole thing stealth camping so i can't really speak to the availability of lodging outside of either prague or vienna. except I would suggest you check out olomouc since it's largely on the way and a truly lovely town (and the hostel there is one of my favorites in all of europe). however, to the best of my recollection there were towns distributed pretty evenly around the countryside, and i would imagine lodging wouldn't be too difficult.