Avoiding/Enjoying the Monsoon in South India this summer

I need some help planning a trip to South India. Basically, I can only take summers (I'm a grad student) at the moment but I desperately want to see South India. I'm arriving in Chennai the last week of June and I'll be there till early August. Terrible time, I know, I know, but that's how it is.

From my research, I've gathered that Tamil Nadu is relatively dry during these months but Kerala gets hammered by the rains. What about Karnataka and Andhra Pradesh? More to the point, where would YOU go if you landed in Chennai in late June? I need some experienced Indian travelers to give me a hand finding the best way to spend my time there. I had a pretty good itinerary for TN and Kerala, but I'm afraid the latter is looking less enjoyable by the day...

On a related note, how much rain are we talking about here? I can never really tell if monsoon means "18 hours of rain a day" or " a couple hours, followed by sun." What's the story on the survivability of the monsoon season in South India? What does it feel like? Are there days where it doesn't rain at all?

Tamil Nadu is probably the only state which would be most drier of all the 4 states.
You could go to visit Mahabalipuram on the way Pondicherry. Stay in Pondicherry for a couple of days.
You could visit Kanchipuram.

Yes, it is possible to get 18 hours of non stop rain, but there are days when it wouldn't rain at all.

It is subjective, but I quite like the rains. Specially when you go to Kerala, it is such a lush state that the rains add to it. The roads aren't that good in some areas so it could also become a bit of a nightmare.

But as I said, western ghats and Munnar come alive during monsoons. There are endless waterfalls and greenery as far and wide as eye can see. I wouldn't suggest you should write off Kerala during monsoons. There is plenty to see and the best part is the rains keep the temperatures down. Being tropical, Kerala is pretty warm and humid during rest of the year.

There is plenty to do in Chennai and surrounds. It depends on what you wish to get out of your holidays.

Thank you for the responses! I was getting a little worried by some folk's advice to avoid Kerala entirely - but now I think this will be a really different, engaging experience in its own right. Maybe I'll end up with most of my time in Tamil Nadu, but I'll still take a wander through Kerala and see how things are.

How's the weather around Mysore during the same time?

I plan on traveling to Andhra Pradesh at the end of June beginning of July. From what I've been told there will just be drizzle around that time. And I hope that's right because I was a little worried about that as well.