Esztergom Castle rises on the same high bluff as the basilica, above the Danube and the Slovak border. The defensive works were gradually dismantled, but enough of the royal palace, walls, and terraces remains to make this one of Hungary's most important medieval sites.
The castle museum explains Esztergom's role as an early royal and ecclesiastical centre. Even if you are short on museum time, come up for the river views and the sense of how strongly the hill controls the town.