In Brasov, my home city :), you can visit:
all the center of the town with the City Hall, the Black and the White Towers, the Black Church (a must!) , the String-Street, and other museums.
the walls of the old fortress and the additions towers (it's a 30min trip)
the Fortress of Cetate (15 mins walk from the center)
the economical area, known as the civic center.
the sky resort (20 mins by special bus, taken from near the city library)
visit brasovcity.ro for other references