Renting a car to drive in India is not a viable proposition for most people not used to this country with its horrendous, chaotic traffic. However, most rent-a-car companies offer chauffeur-driven vehicles that take the hassle out of the visitor.
Avis has a presence both at the airport and in the city. Unlike many local companies, their cars are properly maintained, and they provide roadside assistance, in case of an accident or break-down.
In any case, especially if you insist on self-drive, make sure that you take sufficient insurance to cover you in case of an accident, or unforeseen damage to the vehicle. Often, "full insurance" still leaves you with a hefty excess that you must pay to the rental company, and it may also exclude tyres, windscreen and other features of the car.