I forget which beach. I am glad that it is relatively safe now.
My first visit was 2006. On my return visits in 2008/9 I was accompanied by security who were probably over-protective as well.
As far as my wife is concerned, we travelled a lot throughout Pakistan - perhaps we were too cautious - although we did come up against a lot of anti-Indian sentiment. We found attitudes vary a lot from place to place about a lot of things, and this is no different.
I remember a well educated guy I knew telling me that he stopped going to the Wagga border post near Lahore for fear that he would throw a rock at the Indian border guards in the heat of the moment...
I'm shocked you had to hide her identity in Karachi - usually there and Punjab are welcoming of visiting Indians, esp. if they're your wife