Betty, Helen and JoAnn...this makes me so happy that maybe you can join us! This is the itinerary we're strongly considering:
http://www.amawaterways.com/blue-danube-discovery-2017

Going by their itinerary it leaves the USA on Oct. 6, 2017 (or you can go earlier) arriving in Budapest on Oct. 7. You get on the ship Oct. 9. You disembark and go to Prague on Oct. 16th and fly home on Oct. 19th (unless you want to spend more time in Prague).

The ship is their newest ship, the AMASerena: http://www.amawaterways.com/blue-danube-discovery-2017

Marcie