Origo is my favourite coffee place in Bucharest and I come here every time I get a chance. Not only do they serve amazing coffee, but the design and atmosphere of this place is just great, with lots of subtle details sprinkled all over the place, both inside and on the terrace.
Origo has its own roaster (they also sell coffee to be prepared at home) and is THE place to grab a coffee early in the morning to start your day, an espresso after lunch or an ice latte in the afternoon (ideally on the terrace :D).
It was opened by one of the most famous baristas in Romania and it is situated really close to the Old City centre, but it still manages to be kept a bit away from the hustle.