If you are planning on opening a private bank account in Hungary, you will have to choose from variety of banks, international and Hungarian. You will study the tariffs and packages and see some differences. You should also consider the transaction fees and governmental transaction tax. Note that money transfers inside and outside of the bank are only possible on the working days.
Let's take a simple situation, when a bank account is needed for salary or regular income. Many banks will offer you free account maintenance, provided that the account will receive a monthly amount equal to the minimum wage minus taxes. For example, the most common Hungarian OTP bank has a "SIMPLE" tariff, choosing which, you get free first your of your MasterCard maintenance. You will not be charged for maintaining the account, provided that the details of payment will indicate "salary".
The Hungarian bank card is essential when paying community bills and home Internet. Most Hungarian providers will not be able to accept the foreign card payment. For your convenience, it is worth choosing the way to pay for the services of providers through an online bank or application, since payment by post office, receiving the bill by regular mail is more expensive.
Moreover, having an account with a Hungarian bank, you can establish a regular payment to pay utility and other bills in time. The cost of this service will depend on the selected tariff, in some cases regular payments are included in the package. To get a discount for running a current account, you may also need to keep a certain amount of money on your account, usually the minimum deposit is 50,000 HUF. Such conditions can provide Sberbank in Hungary.
Documents that are required to open an account: passport, residence permit and temporary address card. Many banks will not be able to open an account for foreign clients if they do not have Hungarian address card. If you do not have an address card, you can open an account with the central branch of MKB Bank, the rates of this bank are quite high.
If you are interested in opening a bank account in any other currency then Forint, like Euro or USD, you will be charged 1-2% for the cash withdrawal.
There are very few ATMs, that will issue Euro from your own Euro card without commission. Governmental OTP Bank has only two ATMs in Budapest that issue Euros, one of them is situated in the middle of the shopping district of Budapest.
Useful resource for comparing tariffs for banks: