Around 20km southeast of Utrecht lies Doorn, a wealthy little burg with a claim to an oddment in 20th-century Dutch history: Huis Doorn, a 14th-century castle that was turned into a sort of indefensible mansion during the 1700s. It had numerous owners during its time, but none of them was more infamous than Kaiser Wilhelm II of Germany, who inhabited Huis Doorn in exile from 1920 until his death in 1941.
There's a fine collection of German art that it seems the Kaiser brought with him from various German palaces. Afterwards, stroll the grounds and ponder the fate of the Kaiser, who had been allowed into exile by the Dutch as long as he remained under 'house arrest' (some house, eh?). Catch a local train from Utrecht CS to Driebergen-Zeist, then take bus 50, 56 or 81. It will take about 45 minutes. On national bike route LF4, ride 24km southeast from Utrecht.