Having local currency RON is highly recommended, as card payments are still limited for services such as taxis or public transport.
You can exchange major currencies in any bank or money exchange offices located around the city. Make sure to check the commission for such transaction. There are many places with 0% commission so try to look for those places.
!!! The currency exchange offices situated inside the Henri Coanda International Airport (Otopeni Airport) have in general low exchange rates compared to the offices situated in the city.