The cost varies a lot. Expect to spend between €6 and €10 for the lowest accommodation in a youth hostel in Budapest, although the average cost in a hostel is €20-22 per person.
In Hungary, village tourism is popular and well-developed, and it may be a memorable experience. 1Hungary , National Federation of Rural and Agrotourism, and Centre of Rural Tourism are good places to start your study. There are also rural homes to rent near Budapest, such as the Wild Grape Guesthouse, which provides for a nice mix of seeing the city and a National Park while staying in the same place.