For a city in the tropics, Mumbai has a fairly unusual climate. Some months can be very pleasant and others can be nightmarish for travelers. The rainy season lasts from mid June through mid September, and especially July and August can be ridiculous, with heavy downfall that literally goes on for days, or weeks, on end. The city routinely gets at least partially flooded during this period, and transportation grinds to a halt, so it’s best to stay away.
Conversely, winters can be warm, dry, and pleasant. December and January in particular are marked by warm days with low humidity, and cooler and nice evenings. April and May are the hottest months of the year, and even though there is no rainfall during those months the humidity during the day can be stifling. November through March is definitely the season to go if you can pull it off, and forget about July or August.