Try Rietumu.com.
It’s in Latvia which is in EUROPE and it’s part of the EU.
You can open personal and corporate bank account and it can be done without having to go to the bank by post.
Will cost about 150EUR to open the bank account + get the certificate etc …
The internet banking is stunning, it allows you to send SWIFT payments for 20$. and you can do all your banking online.
The bank account is a true europeen one with an IBAN bank number.
Would highly recommend that one –
Oh and Latvia has bank secrecy.