Hi Rohith, there are many places that you can trek to when in Jammu. The most popular option is to head to Vaishno Devi. The 13 km trek from Katra to the top is a scenic trek with gorgeous views enroute. You can even consider going to Gulabgarh, and trek 32 km up to the shrine of Machail Mata. Some of the noteworthy treks that start in Jammu are Kishtwar to Padum and Kishtwar to Srinagar that passes through Banderkot, Dadhpeth, Mughal Maidan, Chhatru, Sinthan and Daksum. This would take you about 5-6 days to complete. Check out some of these trips for a better understanding of trekking around Jammu:
https://www.tripoto.com/trip/hidden-gem-of-kashmir-alpather-lake-trek-5a8bae512e6f1https://www.tripoto.com/trip/this-trek-through-the-valleys-of-kashmir-is-most-rewarding-5bd70d4b576c7 Happy trekking!