Exchanging money is only permitted in licensed, designated places. Do not take the risk of changing money on the street. You are likely to find yourself with counterfeit money, besides which such transactions are illegal.
The Hungarian National Bank gives official daily foreign exchange and currency rates on 23 currencies.
Most banks have 24-hour banknote exchange ATMs. Besides this there are many credit card and cash card ATMs in operation day and night. Banks and travel agencies can set (and modify) their own exchange rates, taking the bank of issue’s rate as the basis.
Any bureau de change has to have the current exchange rates clearly displayed. Please keep your exchange receipt in a safe place until you depart the country. Broadly speaking, the best exchange rates are to be found close to the rail stations and in the city centre (Petőfi Sándor Street). Banks generally give a middle rate, and the airport and hotel exchange rates are not so competitive.