Well, none of those countries is in Eastern Europe, they are in Central Europe - and Hungarians at least can be quite touchy on the subject. Budapest is equidistant between London and Moscow, and Europe extends a lot further East than Moscow.
A car in Vienna and Budapest will be a pain, (parking in Budapest is difficult), and public transport in both cities is excellent. The train journey between those two cities is 3.25r hours, so a car for that part is pointless.
I think you are aiming for too much - even with 12 days, first day will be lost with jet lag, then travelling will take up a lot of time - Prague is 5/6 hours from both Vienna and Bpest, I cannot answer for Krakow. If you can bear to, limit it to 3 cities, otherwise it be a marathon, not a holiday.