Budapest is two cities that were joined in 1873: hilly, historic Buda on the west bank of the Danube, and flat, lively Pest on the east. The river between them is wide and powerful, crossed by a string of bridges, of which the Chain Bridge, opened in 1849, is the oldest and most graceful. From the Buda side, the castle hill rises above the water with its palace and the spire of Matthias Church, and across the river the neo-Gothic Parliament building stretches along the bank, lit gold at night. It is one of the best-looking capitals in Europe, and it knows it.
The city also sits on a network of hot springs, which is why it has some of the finest thermal baths on the continent. The Gellert baths, in a grand Art Nouveau hotel, the Szechenyi baths in the City Park with their yellow baroque halls, and the older Ottoman bathhouses from the sixteenth century are all good places to recover from a day in the saddle. Old men play chess in the steaming outdoor pools, and in winter the sight of steam rising into the cold air is a marvel. The food is as warming, with goulash, lángos, which is fried dough with sour cream and cheese, and chimney cake from the street stalls.
The ride called the Danube Bend begins here, and it is one of Hungary's best. The road heads north along the river, past Szentendre, an artists' town of cobbled lanes and church towers, to Visegrad, where a ruined hilltop fortress commands a sharp turn in the Danube, and on to Esztergom, where a huge basilica dominates the skyline on the border with Slovakia. The road is gentle and scenic, with long views, vineyards and ferry crossings, though weekends bring heavy traffic.
In the city, riding takes concentration. Trams run on rails that can be slippery, the cobbled streets are rough and parking is limited. Fuel is available at stations throughout the city and on the ring road, the M0. Summer is hot and crowded, and spring and early autumn are perfect, with mild temperatures and fewer visitors. Beware of speed cameras, and leave the bike behind when you visit the baths.