Just back from the 13 July Med cruise with Greece and booked this cruise for next year, although we are not 100% sure we can make it yet from a work perspective.
On this trip we did the Athens on your own excursion through Disney and it was truly one of the best excursions we did. I need to clarify up front that in preparation for our trip we had purchased/downloaded a video course by Dr John Hale from The Great Courses company about travelling through Greece and Turkey. NOTE: do not pay full price for this course if you check it out, they put their courses on sale every couple of weeks. The course covers most of the ports we will visit on this next trip and is an excellent source of research. We also copied the relevant episodes related to Athens, Mykonos and Ephesus to my iPad. The course also includes material on Rhodes, Crete and Santorini among other Greek and Turkish archaeological sites.
When we checked out the Disney excursions available they did not have an excursion that covered all of the sites that we wanted to see. Based on the two 30 minute videos on Athens by Prof Hale, we felt very comfortable checking out the sites in Athens that we wanted to see on our own.
The bus dropped us off at the Arch of Hadrian in Athens around 9:30 am, and we had to return there by 2:30 pm. We quickly walked the short distance to the Acropolis and bought our tickets to get in. Tickets for adults cost 12 each, and tickets for kids cost 6 each, but we had to show their student IDs, not just the kids in order to get the reduced price! These tickets then gave you access to the majority of the sites around the 'rock'.
The queue for tickets was long but moved fast (and was a separate line to the left of the entrance queue). We also chose to divide and conquer, and while DH and DS bought the tickets, DD and I lined up in the entrance queue. And the entrance queue was a massive choke point of people, mostly tour groups, as Rick Steve's describes in his guidebook. We amused ourselves during our wait by watching the stray dogs and cats that are everywhere!
We managed to actually make it through the line up and through the main entrance gate by 10 am (roughly) and then we viewed (when i say viewed i usually mean took pictures of) the Odeon of Herodes Atticus on our way up the hill. Once finally through the Propylaea (another choke point), the view you get of the Parthenon is actually the back of it, and right now it is under heavy scaffolding and re-construction, the 'postcard' view that you probably want is around the other side, near the base on the left as you look at it (which is probably where Mickey was standing in Disney's Greece publicity photos).
After viewing the Parthenon from the entry, we headed left towards the temple of Athena, I.e. the small building with the Erectheion and the Porch of the Caryatids. We wandered around the buildings and checked out the view of Athens, including the long distance views of the Temple of Olympian Zeus, the Arch of Hadrian and the Temple of Hephaestus from high above, from near the huge flag of Greece, took our postcard family pictures of the Parthenon and then headed back down off the 'rock'. Two things to note, up on the Acropolis it is extremely windy and dusty, and leaving the Acropolis takes about as long as climbing up, again due to the choke point at the Propylaia.
Once we broke free of the crowds, we turned right at the bottom of the hill and headed for the Agora. Our tickets from the Acropolis also got us in here as well as at the rest of the sites i will mention. Our main goal was the Temple of Hephaestus, but we also saw the rebuilt Stoa of Attalos and the remaining statues that are all that is left of the Odeum of Agrippa. Note, at the entrance to the Agora there is a water fountain where you can refill your water bottles that you emptied out at the Acropolis, so don't throw the bottles away. Also, when you are required to show your tickets to gain entrance at the sites, pick up a brochure, because although the brochures look alike from a distance, they are each site specific.
Most of the rest of the Agora is pretty much rubble, very ancient rubble that the 'pillar police' will yell at you if you sit on etc (we saw a couple of girls who were using the broken columns for a seat get informed that the columns were history, not props for a photo shoot

.
Next it was on to the Roman Forum to view the Temple of the Winds, a very cool structure with a water clock in it. At that point we took a pass on the Kerameikos and the Acropolis museum as we headed through the Plaka, a long street that headed us diagonally toward the monument of Lysicrates.
We really enjoyed the Plaka, and the shop keepers were friendly and helpful. A couple even showed me other stores to shop at when they didn't have a 'cheesy' enough 'touristic' picture frame for me to buy

.
Once we hit the end of that long street ( and the Lysicrates monument) we headed for the nearby Theatre of Dyonisos, where we could actually sit on the seats etc. Next we headed to the Odeon of Herodes Atticus to see it from a closer vantage point, although if you are short on time you can skip this as you can't actually get in to the odeon as it is still a working theatre.
Heading back toward the main pedestrian street we bought a few bags of nuts that the street vendors sell and then headed to check out the Arch of Hadrian and the Temple of Olympian Zeus up close and personal. The nuts by the way always get special mention from our kids when we ask what they liked about Athens, something about the peanuts with sesame seeds and honey must have really appealed to them, even more than the spicy nuts

. The kids also enjoyed the freedom to roam around , and yes to goof around a little, more than on an official excursion.
Overall, we did not spend anytime inside museums because we were having too much fun just feasting our eyes on everything there was to see and experience on our 'walk around the rock'. And this worked very well for us because my DH and I had watched the John Hale videos a couple of times. As well, my kids are big Percy Jackson/Rick Riordan fans, and therefore they had a point of reference for most of the Greek gods related to the sites we saw. And although Athens around the Acropolis was very easy to navigate, my DH does have an amazing sense of direction

, unlike his DW

.
Another family we spoke to on this excursion had done the Acropolis and the Plaka, including a relaxing lunch in Athens. Overall, everyone made their timings and the bus did not have to wait for anyone. By mid-afternoon we were back on the ship, cooling off in the pool and relaxing on deck.
Something else to consider is purchasing a flip book, sold at most souvenir shops in Athens, for around 10 (I think). The book we bought at the end of our day is called, Athens The Monuments with Reconstructions, and includes pictures of the major sites as they are today with transparencies that flip over top of the pictures and show how the site looked 'back in the day', as well as a brief history/description of that site. It would have been neat to have with us at the sites, but we probably would not have had time to read it on the go.
If we manage to make the 2014 cruise and visit Athens again, we will probably consider an excursion that includes the Acropolis (because it is there and really, it makes a trip to Athens from our point of view) combined with a beach excursion, since it would be hard to duplicate the enjoyment of this trip.