In the morning, explore the ancient Bahu Fort which dates back to the 18th century. The fort is situated on the left bank of the Tawi River and the Shivalik range surrounds it. Visit the temple of Goddess Kali located inside the fort complex. Afternoon, head to the Raghunath Bazaar to buy some souvenirs. Evening, take a stroll at Bagh-e-Bahu for a serene view of the Tawi river.
In the morning, head to Katra to trek to the famous Vaishno Devi Temple. The trek is about 12 km long and will take around 6 hours to complete. Afternoon, visit the Ardh Kuwari Cave, which is about halfway through the trek and is believed to be the place where Mata Vaishno Devi meditated for 9 months. Evening, return to Katra and explore the local markets.
In the morning, visit the Amar Mahal Museum which is a beautiful palace turned museum. It houses a vast collection of paintings, artifacts, and books. Afternoon, go on a picnic at Mansar Lake, which is about an hour away from Jammu. Evening, visit the Bagh-E-Bahu Aquarium which is home to a wide range of aquatic life.
You can also consider visiting the Mubarak Mandi Palace, Peer Kho Cave Temple, and the Surinsar Lake. For side trips, you can visit the famous hill station of Patnitop or go on a day trip to the picturesque town of Udhampur. To maximize your fun, try the local cuisine, especially the famous Dogra dishes such as Rajma Chawal, Kaladi Kulcha, and Ambal. Don't forget to try the famous Gulab Jamuns from Jammu and some Kesar from Patnitop.