Here's a (currently very short) list of banks that serve Euros. More will be added later.
Raffeisen Bank - Central Bus Station
Handily, this bank is right at the end of the bus station on the corner of Rruga Adria and Rruga Egnatia.
OTP Bank - Sheshi Liria
Right across from the Great Mosque, although I've found the ATM to be out of action a couple of times.