Very small, but it contains an interesting selection of medieval weapons (swords, arrows, etc.)
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Turnul cu Ceas
Built in 1360 and standing at 60-m tall atop the citadel hill. Balcony with a great view on the top. It includes a museum of local history with explanations mostly in Romanian.
Biserica Mănăstirii
Lutheran church in late Gothic style, next to the Clock Tower, built starting in 1291 by the Dominican Order.
It's around the corner from his birthplace, within sight of the Clock Tower.
Turnul Fierarilor
Interesting show where they explain the real story of Vlad Tepes in rooms decorated to the story. The story is told only in English, Romanian and Spanish. Mostly a speak show, so it's not worth if you are not fluent on one of those languages.
Casa Vlad Dracul
Alleged to be where Vlad Țepeș "The Impaler" (a.k.a. "Dracula") was born. Now is a restaurant.