Vitamin shop
They call them Vitamin Shops and there is a plethora of them around the city. They sell fresh squeezed juices. It seems pomegranade is a best seller (I never had a pomegranate juice in my life). Other best seller: apple, grapefruit, carrot.
In the cheaper places, the pomegranade juice is a little to acidic... so if you go for it, go to a "good looking" place, or get carrot juice (cannot go wrong with that).