Cash (US Dollars or Euros) can be easily exchanged at any bank or Currency Exchange Office (romanian: Casa de Schimb).
Please note that exchange rates offered by the exchange offices at the airport are quite bad (10% to 25% less than the official rate).
Taxi drivers serving the airport will probably accept US Dollars or Euros, but all stores in Romania will only accept lei.
US Dollars are as good and popular as the Euros.