Here are some lovely spots to explore in November in India
Pune and mumbai
Andaman Nicobar islands
Darjeeling though it will be bit cold
Rishikesh and Haridwar
Mahabaleshwar Lonavala both will be cold
There are many places to see according to your interest and time for example the Gir National Park in Gir Gujarat is the only home to Asiatic Lions and remains closed during Monsoon but is opened after October 15th. Other options are north has good start of Winter in November and Places like Punjab or Delhi and surroundings give perfect opportunity to welcome winter. Then comes the Royal Rajasthan for enjoying Culture and Food remembering the Great Rulers of the Region. If Sea Shores and Beaches are your preference then you can go down south also. If some less visited or unexplored places are on your mind or looking to go far away then North East will open it's doors for you. Choice is yours where to head this November.