Esztergom was Hungary's capital before Budapest was anything, and the Hungarians still talk about it with a sort of quiet pride. Stephen, the first Christian king, was born here around the year 975, and he was crowned in 1000 or 1001, so in a sense the nation begins on this bluff above the Danube. Kings lived in the castle on the hill until the thirteenth century, when a Mongol invasion pushed them south, and the town became the seat of the Catholic primate of Hungary, which it remains.
The skyline is dominated by the basilica, the largest church in the country, a big neoclassical building with a green dome that you can see from far down the river. Inside is the Bakócz Chapel, a small Renaissance masterpiece in red marble that was taken apart and rebuilt when the cathedral was constructed. From the dome you look across the Danube to Slovakia, to the town of Štúrovo, and the two are connected by the Mária Valéria Bridge, blown up in 1944 in the war and not rebuilt until 2001. Crossing it is a small, strange pleasure, with passport-free travel in both directions now.
The riding up the river is a favourite. Route 11 runs along the right bank of the Danube through Dömös, Visegrád and Szentendre, with the water on one side and wooded hills of the Pilis and Visegrád ranges on the other. It is a gentle, scenic road with steady curves, a good surface and plenty of places to stop for fish soup or a coffee. Sundays are busy with Budapest day-trippers, and the town traffic at the Danube Bend ferry crossings can be slow. For more excitement, turn into the hills at Dömös and take the winding roads over the Pilis toward Pilisszentkereszt, where the forests are deep and quiet.
With nearly thirty thousand people, Esztergom has plenty of fuel stations, supermarkets and cafés, and a good thermal bath at Štúrovo if you cross the river. Parking near the basilica is easy for bikes. If you arrive in the late afternoon, climb to the terrace outside the cathedral and watch the evening light on the water. The Danube here is wide, calm and slow, and you can follow a barge for a long time without seeing it move.