I would say that Ceainaria Cinci (which literally translates as Number Five Teahouse) is one of the nicest chill-out places in the city. The teahouse is on the ground floor of a nice hostel, Doors Hostel, in a beautiful house situated in the old part of Bucharest.
You can choose from a huge variety of teas that you can enjoy in a really cozy atmosphere. Inside, there’s a room made out of what would seem to be bunk beds filled with lots of pillows on the floor and blankets (in case it gets a bit chilly during wintertime) and small tables in between. But, if you prefer to enjoy your drink sitting at a table, there’s another room where you can do this, right under some huge plastic mushrooms that ‘grow’ out of the ceiling.
Do take a stroll around the neighborhood as well and you can eventually get to the Palatul Patriarhiei.