Siena is such a place where the weather is temperate throughout the year. Still the people out here do enjoy all the four seasons and it is like; Spring (March - May), Summer (June - September), Autumn (October - November), and Winter (December - February).
So, whether you plan your trip in summer or winter, the weather would be moderate , making this city a round-the-year vacation destination.
However, Spring and Autumn is being considered as the best time to visit Siena.
Best time to visit Natural History Museum Of Siena Or Museo Di Storia Naturale Dell'Accademia Dei Fisiocritici in Siena