I have not been to Chennai in over 3 decades. Having said that, Indian cities in this day and age are basically impossible to ride in. Bring your trainer. In terms of running it depends on where you are in most Indian cities, but unless you get out really early, there are just too many people on the streets. You can't run without dodging a zillion people. It is basically impossible in some locations to even keep up a walking pace. I'm talking about 2 people per square meter density.
Ideally you can find a cricket ground and get used to running intervals on there or treadmill. In some cases I have found quiet side streets that are uninterrupted for 100-400m and just used that section for back and forth internvals (used this approach in China and Taiwan too when in dense city locations....you gotta work with what you have). No idea about swimming, but you are close to the Bay of Bengal depending on where you are so you may be able to swim at the beach.
There should be miles of beaches like this: