So here's the global plan:
Friday: Brno – Ceske Budejovice – Cesky Krumlov, staying in Ceske Budejovice
Saturday: Ceske Budejovice – taking a beerspa in Chodova Plana – Plzen – Nurnberg, staying in Nurnberg
Sunday: Nurnberg – Frankfurt – Koblenz – Cologne, taking the ICE home from Cologne.
The only thing we really have to plan is getting to our hotels and to the beerspa, where are not a lot of trains, in time. The rest of the trip we'll just get out the train where we like and move on when we're bored. Both the Saturday and Sunday require being in the train for about 7,5 hours, so leaving early will give us enough sightseeing time, especially given the fact the 7,5 hour does contain quite a lot changeover time that can easily be combined with sightseeing and trains can be used to do a quick powernap ;)
Eindhoven – Brno (Wizzair): 9€
Brno – Cesky Krumlov (Sporo Tiket): 9€
SONE+ DB / Bayern+Böhmen ticket: 13€
Night in Nürnberg: 16€
ICE from Cologne to Utrecht: 16€