Hey! Its always good to visit a famous hill retreats like Shimla during off season. The weather will be pleasant in the month of October. You can visit places like Jhakoo Temple, Chadwik Falls, take a walk around Indian Institute of Advanced Studies. You can also head to nearby places like Kufri, Shoghi (for some offbeat experience) and Mashobra.
Chadwaick waterfall. Do visit this place as it's beautiful and away from the city.
The Ridge which is the heart of Shimla.
Jakhoo Hills - A temple of Hanuman ji. Also the highest peak of Shimla
Mall road and explore some cafes