I went to pattoki few times and found following nurseries the best in terms of flowering plants specially vines/climbers. Although you will find tons of nurseries but these have got the maximum variety of flowering plants as to my experience. Please note that this extinction does not apply to foliage plants - only flowering plants.
Changa Nursery - 03004580763 - I think the guy name is tariq over there. They had got huge variety of climbers, i bought one wisteria from him and one white buddleia and few aloe veras.
Madina Nursery - 03008483501 - They have got one of the best plant nurseries over there. They had got yellow buddleia(which could not survive because roots of plant went into soil from pot) , Various varieties of Cassia, tangerines, and other climber varieties. I forgot the guy's name who is over there.
Rehman Nursery - Waqar Rehman - 03454743518 - They are specialist of Palm varieties. They also have got some good variety of flowering plants.