The Anna Nagar area, in the northwest part of Chennai, has some decent parks for running. They’re in fairly close proximity, so one can put together a run of decent distance — though the connection between them might not be ideal.
You can do some ~1 km laps around Anna Nagar Tower Park. Then, take 3rd Ave or one of the side streets northeast for ~ 1 km to get over to Bougainvillea Park, which has some nice paths and shade.
- Metro: Anna Nagar East