Goa... would be fun during november. you can enjoy the dcenic beauty of goa. Beaches in North goa... churches in south goa.. club like cabana and mambos, different watersports make your visit memorable and a great experience.
If you want little chilly winds go for Himachal Pradesh - places you can cover are Dharamshala, Dalhousie,Manali,Shimla or the kinnaur range that will have Narkanda,Kalpa,Sangla. If you want beaches opt for Goa is always a best place to visit. You may also go to Mahabaleshwar while returning from Goa via road. Ooty,Coonoor ,Coorg,Kodaikanal has a pleasant weather. You may also plan a trip from Chennai to Pondicherry which will cover up Mahabalipuram and Tirupati.
Hi Suman, November is a pleasant time to visit any part of India be it North, South, East or West. Although, I'm attaching the list of places curated by travelers on Tripoto for your perfect planning. Thanks!