Haven't read the thread, so apologies if this has already been suggested:

Why not take the hydrofoil up the Danube to Vienna? As I recall, it was about a 3-4 hour ride, and very, very pleasant -- scenic views, lots of interesting river traffic, castles on the shore, and the traverse of a lock midway. It departs from the center of Budapest and arrives in the center of Vienna. By the time you're done with taxis, airport check-in and sitting around waiting for your flight, the travel time would be about the same.