Late May through early October is the right window. Spring brings the chestnut trees along Stefan cel Mare into bloom in May; summers are hot (often 28–32°C) but breezy and dry, and the city stays lively in the parks and beer gardens. The grape harvest from late September into early October coincides with the National Wine Day festival, held the first weekend of October on the cathedral square — by some distance the best time to visit if you can plan around it.
Winters are cold and grey, with daytime temperatures around freezing and occasional snow. Skip January and February unless you have a specific reason. The Orthodox Christmas (7 January) and Easter (variable date) are atmospheric in the cathedrals but most other attractions run on a reduced schedule.