I am using NLB bank, which probably is one of most expensive ones, offers internet banking, but only in Slovene. I was checking that other ones offers ebanking in English. Good thing about it is that they have many ATM's and don't charge you for withdrawing money. They have also nice saving accounts.
Well you could ask any former Croatian customer of the Ljubljanska Bank, still waiting for their money back from 1991, when the bank escaped from its customers with their money by renaming itself the New Ljubljanska Bank - or customers of any Slovenian bank who have not paid a bill, and had all their money removed by court order, which happens to such a degree that many Slovenian people would really rather not have a bank account.
For useful Slovenian phrases to deal with such situations see a2z.si/lingotip
I came from Thailand & am living in Ljubljana since May 2012.
I brought money from Thailand and deposited into a Slovenian saving account to be my living expense.
I opened saving account with ABANKA. - Account Maintenance Monthly fee: 1.05 EUR (cheaper than NLB) - Mobile alert monthly fee (optional): 1.50 EUR - ATM Card: Free of charge except if you choose to have fancy picture on the card (extra charge for 7.50 EUR) - ATM coverage: Good as recommended by local people. For me, I see their offices & ATM machines covering the whole center area of Ljubljana. - Internet Banking: Available with extra monthly fee - Credit facilities: Available - Benefits of using ABANKA: Good service from their officers, Many branches, ATM card (with VISA or Maestro) can be used as Debit Card (to pay for goods/services).