Manned locker room at the Sinaia train station. I didn't get prices but it is open from 6am - 9pm daily.

Bucharest North railway station

left luggage (pay 5 lei to leave your bag here for 24 hours).

Bucuresti Nord Gr
Baggage consignment

Constanţa railway station
Left-luggage office 24 hours

Sibiu railway station
Left-luggage office 24 hour

Henri Coanda International Airport

left luggage