October to March is the only comfortable window. Daytime temperatures sit in the low-to-mid 20s Celsius through these months, with cool evenings and almost no rain. December and January can be cold enough at night to want a jacket.
The pre-monsoon (April–June) is brutal: 40°C+ days are routine, the air is dusty, and there is no useful relief until nightfall. The monsoon (July–September) cools the temperature but brings unpredictable downpours. Navratri in late September or October — nine nights of garba dancing — is one of the most exuberant festivals in Gujarat and Rajkot is one of its centres; consider timing a visit around it if you don't mind crowds and noisy nights.