The National Museum of Contemporary Art (MNAC in Romanian) is one of the most forward-looking places in the city. What makes it special among all the other art venues is the location. You’ll find it inside the People’s House, the second largest and heaviest building in the world. It was built during the communist regime and it houses the Parliament, Deputy’s Chamber, three museums, one of the largest ballrooms in the country, etc. You can take guided tours of the building, but visiting this museum is, I think, a highly fulfilling experience of the place.
MNAC is spread across four floors (less if you’re there during an exhibit change or preparations) and you get from one to another by using the exterior glass elevators.
The current collections are described here. It is always a good idea to check them often as they change quickly.
If you’re lucky, there are also occasional parties and festivals taking place in the museum, I’ll add them here as they’re announced.
I recommend visiting the place at sunset as it has one of the most beautiful vantage points in the city.