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Hisor fortress (also spelled Hissor, Gissar, etc.) is a partially-rebuilt Silk Road fortress located not too far from Dushanbe. It was the seat of the Khanate of Bukhara's power in Tajikistan, and was captured by Alexander the Great and Chinggis Khan. Across a square from it is a madrassa and the foundations of a caravanserai, but neither of those have been restored (but they can still be toured).
Gurminj Museum, Музей музыкальных инструментов
This small museum has an interesting variety of Central Asian musical instruments as string instruments example: rubab, Pamiri rubab, tanbur, dutor, setor, qashqar, and ghizhak. There are also number of drums such as tabl, daf, and doyra. That alone is worth a peek if you like instruments, but better still is to go when a musical or cultural event is being held, or hope to catch the folk musicians who practice there and can demo many of the instruments in the collection.
Национальный музей древности Республики Таджикистан
This museum offers four floors detailing the history of what is now Tajikistan, primarily through art. The basement covers prehistory, including the geology of the country, while human history starts on the ground floor and increases chronologically as you ascend to the next floors. The ground floor is home to the crown jewel of the museum, the giant Buddha in Nirvana statue found in Ajina-tepe, as well as numerous historical artefacts from each empire to have set foot in the country. The upper floors detail Tajikistan's history post-Russian conquest, while the final floor is a gallery of paintings and sculptures made during the Soviet era, including a display of Soviet films filmed in Tajikistan.
Tajik:Ҳайкали Исмоили Сомонӣ, Russian: Арка и памятник Исмаилу Самани.
A monument to the 10th-century founder of the Samanid dynasty. This statue commemorates the one after whom the currency is named. Apparently, the crown is 10 kg of Tajik gold. Beware: the police at the bottom may ask for money if you take photos, so stand far back and use your zoom. (And don't encourage this bad behaviour.)