Least crowded, calm and quite places will be Raja Bazar, Pir Wadahai, etc. because their crowded will have shifted to zoo, Daman-e-koh, Rawal Lake and Murree.
In all seriousness, if you MUST go, then take your food along and go past Pir Sohawa. Around 2-3 km afterwards, there are several spots where you could sit in the shade, in a rather secluded area, for a nice picnic. There is going to be a lot of rush on the road though.