Kashmir is known as "heaven on Earth" and its a paradise indeed. A place that you should definitely visit once in your lifetime. The place, the people, their attire, their accent, their culture, their beauty, the weather, everything is so refreshing, that you would always want to go and visit it again. And to experience the beauty of this heaven, there is no bad season. Every season will surprise you with its unique beauty and colors.
Jammu and Kashmir is located in northern part of india. If you are planning your trip for around a week or less, I will personally suggest you to only cover Kashmir and come back for Jammu in a separate trip.
To start with, you can book a direct flight to Srinagar. The views from flight itself are enchanting.