I have been with PrivatBank for a number of years now. It is the biggest in Ukraine. ATM access is available widely. The problem I had was setting up an account as a foreigner. If you are not a Ukrainian citizen you will need to get a tax number. I initially queued up at the office in Odessa but found this a lost cause on a hot, sweltering day and gave up after waiting an age. I eventually hired a lawyer to do this for me and my tax number was posted to me in the UK. You will need your passport translated for this too. When I managed to open a deposit account the interest was 23% but is now down to 16%. However, that is still a lot better than you can get in the UK. It is not easy to deposit cash into your account either. For non resident's, proof must be shown of the origin of the cash (eg. ATM receipt and the card it was withdrawn on). Online access is available through a phone number on Privat24.