Budapest is two cities that were joined in 1873: hilly Buda on the west bank and flat Pest on the east, with the Danube between them as the main street. The Chain Bridge, opened in 1849, was the first permanent crossing, and the lions on its ends were said to have been made without tongues, a story locals find funnier than visitors do. Above it, on Castle Hill, stand the royal palace and the Matthias Church, with its patterned roof tiles, while on the Pest bank, the Parliament, finished in 1904, sprawls along the water like a Gothic wedding cake. At night it is lit gold, and it is one of the great sights of Europe.
The city sits on hot springs, and bathing is a cultural habit more than a tourist attraction. The big baths, Széchenyi in the park and Gellért under the hill, are places where elderly men play chess in the water and families stay for hours. The city also has the oldest underground railway on the European continent, the little yellow M1 line, opened in 1896. Food is paprika-heavy, with goulash, chicken paprikash and fried bread called lángos with sour cream and cheese, and the old Jewish quarter in Pest is full of bars set up in half-ruined courtyards.
On a motorbike, treat the centre as slow. Tram tracks cut through the streets, cobbles are slick when wet, and drivers are quick and a little impatient. The Buda hills offer some of the best city riding, with tree-lined roads climbing to viewpoints, and you can be out of the suburbs and into the forest in thirty minutes. North along the river lies the Danube Bend, with Szentendre, Visegrád and Esztergom, and it is where most Budapest riders go on a fine weekend. Motorways such as the M0 ring, the M1 and the M3 need an electronic vignette, which is easy to buy online or at a petrol station.
Fuel and food are no problem in a city of nearly two million people, with filling stations on every ring road. Choose accommodation with secure parking, as theft of bikes is not unknown. In winter, snow and ice are possible, and in July the heat on the tarmac can be intense. Go for an evening ride across the bridges, when the lights come on, and you will see why people stay.