This is not about a single place. Bucharest - and Wallachia for that matter - hosts many small pastry shops (Ro. patiserie); usually the farther you go to the North (Transylvania, Bukovina, Maramureș) and West in Romania, they are fewer, without any disrespect for people living there.
A piece of notice is needed here however: a few years ago a company originating in Timișoara brought a Fornetti franchise system in the country. They pretend they sell pastry. Actually it is frozen dough with (very little and often tasteless) filling that they bake straight out of the fridge. This has nothing to do with the traditional stuff. Even though they spread more and more, with a good marketing campaign against independent, small pastry shops, I do not recommend them. This has nothing to do with real pastry and here for one Bucharest with its traditions wins at points. Romanian pastry is based on dough made on the spot and baked shortly afterwards, hence its being crisp and tasty. A similar piece of warning goes for the Gogoașa Infuriată chain as opposed to local donuts, which are bigger, fatter and tastier (personal opinion); read below about one of the last places that sell local donuts.
As for pastry shops, there are many of them, but my favourite one is a small outlet on 71 Calea Dorobanților (near the crossing with Slătineanu Street), the Tahina (see the picture above); their pumpkin strudles and ‘palmieri’ are absolutely delicious. It is also a place that would teach lessons the big smart PR wigs of the moment, with the always smiling lady there, hence my returning. I also give a special thumb up for the pastry shop on Tache Ionescu Street, across the street from Yeshua Tova Synagogue; their meat or salted cheese pies are fabulous, even B&R appreciated them as top while getting his hands oily. There are many others, but I have to mention the one on Smârdan Street close to Șelari Street or for the one at Piața 1 Mai bus stop, around the corner from the shawarma place. Or for the ones near București Nord railway station (the one on Calea Grivțtei, 50 m. NW off the crossing with Duca Avenue is great). Or the one across the street from the Academy for Economical Studies’ main entrance, on Dacia Avenue (and a new one on the same side of the Dacia with the entrance, between the ASE and Romana Square)... And the list can go on for a while. As for Oriental pastry, one of the best shop for baklava in the city lies on Vatra Luminoasă Street, 200 m. East of the crossing with Mihai Bravu Avenue.
There can be salty pies (pastry filled with salted cheese, mushrooms, minced pork, spinach, cabbage and even sausages), as well as sweet ones. They are very diverse here, from pastry filled with apples, pumpkin, peaches, berries, walnuts, sweet cheese, Turkish delight, jam, vanilla cream or chocolate, and all the way to a full baked apple in dough. The salted or sweet cheese or the meat filled pie sold by the kilo is harder and harder to find unfortunately, but the small confectionery shop on Gheorghe Magheru Avenue (close to Piața Romană, located 50 m. North of the KFC) still sells it, together with great cakes and some other pastry, including a different, way larger kind of baklava I like very much. Some places also serve delicious donuts (Ro. gogoși) or langoși (donuts filled with cheese, chocolate, jam). These are fewer and fewer unfortunately. One of the last joints selling real local gogoși and langoși lies at the crossing of Ion Câmpineanu with Academiei streets (opposite Union Business Centre, near the post office).
GPS - Patiserie Tahina - N44 27.073 E26 05.929
GPS - Patiserie Șelari - N44 25.836 E26 06.040
GPS - Patiserie Gara de Nord 1 - N44 26.802 E26 04.602
GPS - Patiserie Gara de Nord 2 - N44 26.883 E26 04.507
GPS - Patiserie Tache Ionescu - N44 26.658 E26 05.860
GPS - Baklava and Turkish sweets - N44 26.321 E26 08.411
GPS - Gogosi Campineanu - N44 26.231 E26 05.914
GPS - Patiserie ASE - N44 26.819 E26 05.855
GPS - Patiserie Dacia - N44 26.806 E26 05.879