October to March is the comfortable season -- daytime highs around 25-30C, cool evenings, very little rain. April and May are punishingly hot, regularly hitting 40C and above. The southwest monsoon arrives in late June and runs into September; rainfall is moderate by Indian standards but humidity is high.
The single best reason to time a visit is Navratri in late September or early October -- nine nights of Garba and Raas, the traditional circular dances, performed in halls and open grounds across the city. Vadodara, along with Ahmedabad, is one of the centres of the festival in Gujarat; the United Way of Baroda Garba in particular draws tens of thousands of dancers a night. Book accommodation well ahead.