In a cave within a forested mountain rising steeply above Katra, the Vaishno Devi Shrine was popularised in the 1990s songs of Gulshan Kumar, and has since become one of India’s busiest pilgrim sites. These days it attracts millions of domestic visitors, though the appeal is a little hard to understand for most non-Hindus.
The climb is around 12km on foot using mostly covered walkways with shelters and accommodation available en route, though it would be possible to get up and back in one long day. You need to register (free) by showing your passport at the shrine board office beside the Tourist Reception Centre: queues can be very long but move fast with over 20 handling desks at work. The pass you receive is valid as long as you start within six hours.