The best seasons to visit Mussoorie is between April to June and again during September to November. When the plains of North India experience heat waves, Mussoorie provides a welcome break. September - November is spring time here. During this season Himalayas are clearly visible. It is better to avoid monsoons as the roads to Mussoorie are in bad shape.
Same thing applies for the winter when roads are blocked due to snowfall.
The nearest Airport to Mussoorie is 60 kms away from the place. The airport is called Jollygrant Airport but there are no regular flights to this place. As such Mussoorie does not have a direct rail link. Dehradun Railway station serves for Mussoorie too. This station is linked which Superfast trains to other major cities in country.