We are staying in Prague for one week and have an extra 3 days to fill before returning home. Budapest? Dresden? Venice? Is a side trip by air from Prague feasible cost wise?
Any suggestions appreciated.

To each his own, but you're talking major cities - - and my inclination in this situation would be to get out and some of the rest of the Czech Republic. The five destinations mentioned here most often are Cesky Krumlov, Kutna Hora, Karlovy Vary, Telc and Olomouc. Never seems to be much mention of Jihlava or Brno (plain old 20th century cities?)

Or the Silesia area of Poland was nice - - we spent way too little time there on a whirlwind overnighter excursion this past May.

Best wishes,

Rex

These mentioned by Rex are good for day trips from Prague.

Of the three you mentioned yourself I think Dresden is your best option since it is very easily and quickly reachable by train. Also, there is a stop between Prague and Dresden with name Bad Schandau, which is located in very scenic surrounding (National Park, bizarre sandstone rocks, vast forests). What about this nice and romantic rural area? But I might be biased since I am a Dresden resident

Rex had good recommendations. Budapest is an 8-hour train ride so, unless you flew, would take up a lot of time. Dresden is just 2 hours north and Berlin just 2 hours from Dresden. I would go to Dresden for a day and then to Berlin for 2--not really enough time but Berlin is spectacular and Dresden is very interesting.

Slovakia!