In Bucharest you could visit the Palace of Parliament (one of the world's largest&most useless buildings), the Village Museum (old traditional houses brought from villages throughout the country and displayed in one of the large parks in northern Bucharest) and the old quarter (a small surviving part of pre-20th century Bucharest, it has a few landmarks worth seeing and dozens of clubs, restaurants, bars etc.) - this should take about one day.

Spend the rest of the time in southern Transylvania, preferably in/around Brasov (a historical city about three hours away from Bucharest by train or car). Along the way to Brasov stop in the mountain resort Sinaia to visit the Peles palace (the former summer residence of the Romanian kings) and maybe do a bit of hiking into the Carpathian mountains

Then once you get to Brasov explore the city's well preserved medieval neighborhoods and try to do some side trips to the tourist sites around Brasov, like the so called Dracula's castle in Bran (~40 minutes away by bus), the fortified churches in Harman or Prejmer (30 minutes away).
You could even try to do a day trip to places a bit further away like Sibiu (the other major historical city in southern Transylvania, 2 1/2 hours away from Brasov) or Sighisoara (one of the few actually inhabited medieval citadels in Europe, about 2 hours from Brasov).