To be honest with you the monsoon season isn't the best time to be visiting India. First of all, the chances that it will rain all throughout your holiday is high. The other issues that would occur are that, you won't really be able to visit any outdoor tourist places, which includes shopping. If your someone who would like to visit national parks and sanctuaries, it is most likely that they will be closed during the monsoons. Weather-wise, it will be very humid and sticky, and if your sightseeing outdoors it would not really be a pleasant time.
I would suggest visiting during the winters which is from November to February, or in the month of April or October.