Every year in July, Sighisoara hosts the Festival of Medieval Arts and Crafts which recreates the medieval atmosphere of the town.
The Cidadel which is the UNESCO Site can be seen in about 4 hours. I suggest staying one night and then travel to Sibui and spend at least 2 nights there.
I stayed at Villa Franka on Decembre NR 1 which is across the street from the path to the citadel. It is an 1894 Villa, very comfortable with an excellent breakfast with homemade jams. Staff are very helpful.
Sites to see are: the Church on the Hill with 500 year old frescos, the Church of the Dominican monastery known for its carved altarpiece, baroque painted pulpit and it's 17th century organ and the 14th century Clock Tower (this tower controlled the main gate of the half mile long defensive wall). The Clock Tower houses the Museum of History which holds a medieval pharmacy from 1670, fine arts and a collection of clocks. There is a walk up creaking, winding staircase with views of the red-tiled roofs of the Old Town.
Walkway to CitadeL
The large Basilica along the river with view from Citadel
Close up of Clock Tower
Clock Tower from the top
The Wall surrounding the Citadel