October is a great time to visit most of the parts in India.
Coorg, Hampi, Munnar, Pondicherry are some. A one week trip covering all these places can also be made. There are also some national parks. October is a good time to spot the wildlife. Bandipur National Reserve of Mysore is a famous one.
Goa becomes very green and active after monsoons. This is when it begins getting into party mode. Gujarat and Rajasthan tour is another great option for a 10 day tour.
The monsoons in the East are magical. One can explore about 2 states in 10 days, and it’s surely worth it. Also West Bengal can be a good base to move further.
North begins it’s winters in October. With early days of snow about to begin, Dharamshala is a great place to spend days. One can also visit Rishikesh, Kullu-Manali, Spiti valley.