I basically agree with James. I did this exact trip 2 years ago and loved it!
Day 1 Arrive in Prague....take it easy. Stroll Wenceslas Square to the Bridge/River
Day 2 Prague...Focus on the Castle/Church and Lesser Town
Day 3 Prague...Focus on the Main part of town/Jewish Area
Day 4 Bus to Cesky Krumlov....stroll the castle grounds to get a lay of the gardens
Day 5 Full Day in Cesky Krumlov (I only spent 1 night, and was sorry. Take a tour of the castle baroque theatre. Take a raft down the river!)
Day 6 Bus to Vienna...get a lay of the land doing the ringstrasse/walk around downtown
Day 7 Vienna....take a tour of the opera house/enjoy the sights
Day 8 Vienna....take a train to Melk and bike the valley....evening back in the city
Day 9 Day trip to Bratislava (take the hydrofoil boat there, and the bus back)/evening in back in Vienna
Day 10 Budapest....my favorite city: take a dinner cruise as a hello to the city (I prefer the music on Silverline/also liked Legenda)
Day 11 Budapest....a day for the Pest side....enjoy one of the baths in the afternoon
Day 12 Budapest....a day for the Buda side!....Don't forget Gellert Hill/cave church/Buda Castle/Matthias Church/Fisherman's Bastion
Day 13 Budapest....mix it up. Take a tour of Parliament. Treat yourself to my FAVORITE restaurant ever: Zeller Bistro! (Don't miss the foie gras appetizer or the duck entrée!!)
Day 14 Budapest....make sure you stop by the Central Market Hall for great cheap food and souvenirs.
I am in love with Budapest now, and am planning my 3rd trip in September with my Mom and Aunt (who have never been to Europe). I insisted they try Budapest, and you'll soon know why!