Pickpockets are all too common throughout Europe and not just in Athens. If you are goin(g to get all worked-up about this kind of thing you might want to either stay home of spend the big bucks for the cruise line excursions. Athens is actually a fabulous tourist city (we were just there a few weeks ago) and personal crime (such as pickpockets) are not a big deal for those that take simple precautions and use some common sense. The cheapest (and often fastest) way to get into central Athens from Pireaus is to take the train less then $3 which becomes part of the underground metro (subway) system once you get near the city. Once you arrive in Athens you can transfer to the other metro lines at no additional cost which means you can change to the metro line that takes you to the station near the Acropolis. Getting from the ship to the train station (in Pireaus) can be accomplished by walking (about 25 min) or using the local bus (accross the street ro the port). The bus ticket is now the same as the metro ticket which means 1 ticket (I think its bout 1.40 Euros) can be used for the local bus...train to Athens and the Athens metro lines. I think the ticket is valid for about 90 minutes (once you validate it).
As to the Acropolis (we were just there last month for our 3rd visit) there is a lot of restoration work at the current time...but it causes minimal problems for visitors. We strongly recommend visiting the new Acropolis Museum (located near the Acropolis entrance) which will really give you a better appreciation of the ruins (much of the treasures from the Acropolis are now housed inside the gorgeous museum building). For walkers, its relatively close to walk from the Acropolis to the popular Placa district.