since you are so limited in both time & mobility, you probably should book a car service that will pick you up right AT the cruise ship & take you into Central Athens, to a cafe with a good Acropolis /Parthenon View, and just wait for you to sit outdoors & have a snack or lunch or whatever, then drive you around to a couple of Views (such as the 1896 Olympic stadium, and thru Syntagma Square by the Parliament (former Kings palace), etc... best to do a little homework on this... and then take you to the airport.
It wont be cheap, but you are very limited, and you also will have luggage -- do you think you can fit all your (BIG) cruise luggage for 4 into a 4 door sedan? Or would it be wise to rent a larger vehicle? Two reliable outfits to check on internet are WELCOME PICKUPS And CITY CAB -- both are car services, although they may use licensed taxi driver as part of their fleets. You canget the cost estimate beforehand and pay via credit card, thus no surprises... and all drivers of these outfits are fluent in English.
Once you've decided on a strategy, we can come to you with specific cafe suggestions -- its best to choose ones that hav e a good view both from outside tables & inside by the windows -- a sunny De cember day could be pleasant outdoors, even 60 deg F... or it can be cold and rainy. Luck of the draw.