If you're looking for city life then it's Srinagar and if you're looking for mountains and scenery then there are some best place you can go with you family and can stay there as well E.g Sonmarg, Gulmarg, Pahalgam, and if you are into trekking like to go to places full of adventure and mountains and hidden alpine lakes then there are countless places.
‘ Doodhpathri- Budgam in Srinagar’
Doodhpathri is the place to visit in summers, if one wants to experience the real beauty of Kashmir - the endless green meadows, the vast expanse of Pine trees, the snow capped mountains and the gurgling, gushing mountain stream. It is still unexplored. Not many tourists go there. Doodhpathri is at a distance of 40 Kms From Sheikh ul-Alam International Airport and it takes about 1 hour by Car.