I will go to Romania soon and I'm a beginner as a traveler. I don't know where I can exchange Euro to Romanian Leu cheaply. I know it's not recommended to exchange money at airport. So at which bank do you recommend to exchange money there?
When I was last in Romania in 2007, there were exchange bureaus around the big cities such as Bucharest and Brașov. They were generally well-run and secure. They had their rates posted right outside.
You might find people on the street or in the train offering to exchange money with you. Don't do this. You're going to get ripped off. Either they'll run off with your money, or they'll give you a terrible rate.
However, my recommendation (and what I did in 2007) would be to use your debit card and get money from an ATM. You might lose a bit in fees and the exchange rate, but probably a lot less than you think. You'll definitely lose less that way than if you bring along a wad of cash and somebody steals it. There are probably still problems in Romania with pickpocketing and other types of thievery, so I'd definitely take the potential 2-3% fees from an ATM over the potential loss from bringing over a lot of cash and having it stolen.