Hi, in case you don’t have time for Srinagar (Kashmir Valley) which needs about 4 to 5 days, you may consider Patni Top, a hilltop tourist destination about 85 km from Katra after darshan of Mata (you can even enjoy paragliding there). No package is required, you may travel on your own making arrangements after some research online.
Https://tripoto.page.link/hKqqjcLhaMbU2Rxp7 Kindly check the above Tripoto link for details. Vaishno devi is also known as Trikuta and Ambe. It is a Shakthipeeth temple located in Katra Jammu Kashmir. Though packages are available, many travel on their own to the temple.