Esztergom, an ancient and lovely city on the Danube, overlooks Slovakia (just across the river). Plan at least an hour to see the huge 19th-century basilica perched dramatically along the river, and the Christian museum where ancient books and art are displayed.
Other sites of interest include the Hungarian Waterworks Museum (history of the Danube River), the Balassi Balint Museum (ancient Turkish coins) and a castle (which includes a museum). If you're traveling in the summer, consider taking a riverboat between Budapest and Esztergom, which is 25 mi/40 km northwest of Budapest.
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