
Dushanbe is the capital and largest city of Tajikistan. Dushanbe means "Monday" in Tajik, and the name reflects the fact that the city grew on the site of a village that originally was a popular Monday marketplace.
There is not much "to do" in Dushanbe. You can visit the Museum of Antiquities on the main square. It is quite old fashioned, and include a number of exhibits that detail the country's history. See Sleeping Buddha in the Museum of Archeology.
In general, Dushanbe is a safe. Robberies and street crime does occur -- even in broad daylight -- although this is rare. The police force is almost totally ineffective, which can lead to criminals acting without much fear of consequence. People keep to themselves; they are very private; you cannot even ask someone the time. Although some are friendly, people (both Russians and Tajiks) can be quite rude and unhelpful.
If you are a woman, be careful. Be prepared for harassment, not just verbally. Be prepared for a lot of staring from large groups of men and even "groping" on public transport (just to get thrills of touching ones skirt or something). Take care as a woman!