One thing I can say about Athens... this is a city that you could visit without spending too much of your money. The port we docked at, Piraeus, is the port neighborhood of Athens. Athens is a seemingly never-ending metropolis, and Piraeus is where the sea of white rooftops ends at the Aegean Sea.
We got off the ship around 10 AM to walk along the port counter-clockwise until we saw the pedestrian bridge that allows access to the Metro. It's about a 20 minute walk with not very much to see, but the fresh air is just something we couldn't take for granted. We got off at station Omonia and switch to the red line that goes to the Acropolis.
At the Acropolis station, we got off and went directly to the "Temple of Zeus - Olympiéon" (walk east) and bought the 1.20 € that took us straight to where we needed to go. We visited the Temple of Zeus and then walked west toward the Acropolis. In my opinion, the Acropolis is the best place to visit in Athens.
Exiting the Acropolis, you can climb the Mars Rock for a nice picturesque view too. We walked down to the Old Agora and found a lot of things to see there too. Exiting North, you will be in the Plaka. This is a part of the city that has a lot of small streets filled with restaurant, shops, etc. Once we got tired, we walked down the north side of the Acropolis, stopping at a café in the Anafiotika neighborhood on one of the steep, narrow streets lined with cafes and restaurants. This shady and picturesque street (Mnisikleous Str.) made for a great place to rest the legs, relax with some food and drinks, and check up on e-mail with free wi-fi. We really enjoyed ourselves at Anafiotika over the last few hours.
We made our way to the Hadrian's Library (more ruins) and then wandered around until it was time to take the metro back to Piraeus since it was a straight shot (about 4-5 stops) and only a couple euros a person. The train station is about a twenty minute walk from the ship, but that wasn’t a problem at all. Upon arriving back in the room, we all crashed for an hour nap before enjoying the sail out of Piraeus into the deep blue Aegean Sea from the comfort of our balcony.