Flew in/out of Prague on BA and used a "European East" train pass, which was easy and comfortable. All cities have fantastic public transit.
Prague: Beautiful town, but buy a SEPARATE book of maps. Liked: cruise, early morning walks, Jewish quarter, and picnic supplies from "Bakeshop" just off Old Town Square. AVOID the rude staff, construction, and inability to honor pre-paid reservations at the Prague Marriott. Tourism is low and we found locals to be almost hostile in many places. Warning: cobblestone streets EVERYWHERE so bring comfy shoes. Also, if you are a museum person, go someplace else. Prague is about cafe culture, beer and architecture.
Budapest: Beautiful, diverse, friendly and cosmopolitan yet inexpensive "Paris of the East." Highlights: "Absolute Walking Tours," Szechenyi baths, seeing an opera, and the House of Terror museum. Picnic food: "Hummus Bar" which had the best falafel I've ever eaten. Budapest Marriott: 5 stars at 2 star prices, including most meals. Lowlights: we had to leave.
Vienna: Its very efficient, but (gasp) kind of sterile. Enjoyed a chamber concert at MozartHaus, Hofsburg Palace, and the Naschmarkt (unbelievable open air market). REALLY expensive ($6 for a latte) and the vibe there was all business.