I visited two markets whilst I was in Chisinau, although there are several, in the city and its environs. The main central market that I was aware of, is on Strada Armeneasca (Armenian Street) was the closest to a large locals market. I believe it goes all the way through to Strada Tighin on the other side but I didn’t spot an exit this way (however this may have been just as well as I think we would have been quite disorientated by this point). It is a large market where the locals shop and sells virtually everything you need from fruit, groceries, clothes and household goods. You can purchase eyelash curlers, shoes and laundry detergent if you so wish. In the end I just purchased a leather belt for the equivalent of £4 (I wonder if locals would pay the same, but I was happy with the price). As a true locals market, you only get locals here, so not everyone will speak some English. What I liked most about it was the snapshot of local city life.
Not far from Armenian Street, on the main drag (Boulevard Stefan cel Mare) by the junction with Strada Mihai Eminescu, is a good art and craft tourist market. There are some pretty paintings, but nothing eye catching (Moldovan art doesn’t have a distinctive ‘style’ that you can identify), mainly still life, portraits and local scenes. This is also the place to buy Russian or Ukrainian nested dolls. The Ukrainian versions apparently have different designs within in. As well as traditional painted ones you could get ones with political figures (Obama or Merkel for example) or animals. There are also Soviet ‘antiquities’ such as hats and badges and a limited amount of embroidered craft goods. I didn’t make any purchases as nothing really grabbed me, but prices seemed reasonable. It is open air, so weather could have a factor in its appeal!