Athens city is a 20min drive inland from Piraeus port so you need to organise a bus/taxi. We booked a simple return bus from the boat and made our own way up to the Acropolis. Again, do this first as it gets unbearably busy up there soon after all the cruise ship organised tours arrive. Be sure to visit the new Archeology Museum at the foot of the Acropolis - it's very interesting and the air-con is great!!
There is plenty of shopping in the old narrow streets and plenty of air conditioned bars and restaurants.