I will spend 3 days in Chisinau so with a buffer that is 4 days total.
Chisinau was founded in 1436 when a monastery was built. In the 16th century the Moldavian Principality fell under control of the Ottoman Empire. By the beginning of the ninteeth century it was still nothing more than a small village. In 1812 the Russians occupied the city. The population began to grow. The town played an important part in the war between Russia and Turkey; Chisinau is where Russia based their operations. Many Jews choose to settle in the city towards the end of the nineteenth century due to promising economic conditions. From 1918 to 1940 Romania held the city. Much of the Jewish population was murdered during WWII. After the war it became part of the Soviet Union. Today it is the largest industrial center in Moldova.
Things to Do:
National History Museum of Moldova- This museum is so well done that you might think that Moldova is the center of the universe. The most interesting section is on WWII battles.
National Museum of Ethnography and Natural History- This museum traces the countries cultural and natural heritage. Check out the dinosaurs.
Day Trips from Chisinau
Circova- This is a vineyard. Usually only groups can visit, but begging goes a long way.