Budapest has a very good public transport system, consisting mainly of the metro (currently 4 lines), tram and buses. The fares are rather cheap compared to Germany. As a tourist you can visit practically all sights in Budapest by public transport, a car or even a rental car is hardly necessary.
Tickets and fares public transport Budapest
All EU citizens over 65 years and children under 6 years of age can use the public transport of Budapest free of charge.
All prices and exchange rates as of June 2019:
Single ticket: 350 Forint (about 1,10 Euro), be careful when changing trains, you usually need a new ticket in Budapest.
Ticket for 10 people: 3000 Forint (9,20 Euro)
Airport bus single ticket: 900 Forint (2,80 Euro)
Transfer ticket: 550 Forint (1,70 Euro), with this ticket you can change trains once in Budapest.
24-hour ticket: 1650 Forint (5 Euro)
72-hour ticket: 4150 forints (12.80 euros)
Weekly ticket: 4950 Forint (15,20 Euro)
Monthly ticket: 9500 Forint (29,20 Euro)
So the prices of tickets in Budapest are much lower than in Germany. A monthly ticket costs about as much as a weekly ticket in Berlin.
Where to buy tickets in Budapest ?
There are extra ticket counters at large stations. At the subway stations and many tram stations there are vending machines. If there are no vending machines, you can usually buy tickets from the driver, but they are more expensive. Single tickets then cost 450 instead of 350 forints.
Budapest Metro (subway)
It is the oldest metro on the European continent. For some years now there has been a fourth line. About 80% of all sights can be easily reached by metro in Budapest.
More info: Article Budapest Metro
The tram network of Budapest has become smaller, it is more and more only a feeder for the metro. Theoretically there are still about 40 lines according to the timetable, but many of them run on the same tracks or only at certain times. But the tram is still an important means of transport
There are still countless bus lines in Budapest. These mostly operate in the suburbs and suburbs without metro or tram. As a tourist you will usually use the metro the most, sometimes the tram and rarely the buses.