Mathura is a laid back temple town that offers you a very peaceful experience. You can go during Ganga Dussehra, in May, or Buddha Purnima. Both times see some very beautiful activities at the Ghats (Read More)of Mathura. Visiting during February-March, for the Holi celebrations at Nandgaon, Barsana and Mathura, is a different experience altogether. Holika Dahan here is also a great attraction in Mathura.
Get to Katra from Srinagar first. You can then go to Vaishno Devi, and complete one part of your trip there. You can then come back to Mathura via a Srinagar-Delhi flight.