Hi from Wisconsin,
For a day trip, let suggest Konopiste Castle. Trains from Prague to Benesov u Prahy run nearly every half hour. The Cost is about 6 euro one way. From the train station, the castle is about a 30 minute walk. For train info use cd.cz. This website has the best prices and you can print your own ticket.
Why THIS castle? I have been to many castles over the decades. I loved seeing the remains for castles built by King Richard in France and the impressive castles of Edward in Wales, but they are empty, nobody has lived there in centuries. Konopiste is as if Franz Joseph just left to go hunting this morning and will be back for supper. True, the castle is 'modern' with early flush toilets, but he was the heir apparent to the Hapsburg crown when he was assassinated in 1916 and he kept things up to date in his home.
This is more a castle to show wealth and power than a defensive structure. His collections of armor, guns, and trophy heads (!!!!????) are worth the trip.