Athens Advise

The driver will take you to the center of Athens, passing by the marinas of Piraeus, which are right next to the cruise port. There's no real "tour" of these places unless driving down an avenue can be considered a tour.

As specified, the Parthenon, the Erechtheion, the Temple of Athena Nike, the Theater of Dionysus, and the Odeon of Herodes Atticus are all on the Acropolis Hill, accessible with a single €30 ticket. This ticket must be pre-booked with a specific visit time, otherwise you risk waiting in long lines during peak season or even not being able to enter.

Is the Acropolis & Slopes entrance ticket included in this tour?

1 hour 45 minutes to visit all these places is optimistic, unless you're just taking a few photos and selfies.

15 minutes to see the Temple of Zeus is a good estimate; the driver will drop you off in front of it, you'll take a few photos, and then return to the car. Done!

The Panathenaic Stadium would take about an hour to visit, but the driver will stop in front of it, probably for a minute.

The changing of the guard ceremony takes place every hour in front of the Parliament on Syntagma Square. Same principle as for the other places. You get out of the car, take a few photos, and return to the car.

Then you'll go to Mount Lycabettus via streets and avenues, passing what they call the "Athenian Trilogy."
Here too, some beautiful photos of the view of Athens and then return to the car.

Is it worth it for €250? It depends on what you're looking for.

The Piraeus marinas and what they call the "Athenian trilogy" are just marketing fluff.
The same route done on your own using taxis and public transport would cost about five times less but would require very good planning skills ahead to fit in 5 hours.

The approximately €200 difference is because you won't have to do anything other than be taken from one place to another in an air-conditioned car just like you go from one port to another but on a cruise ship.

Thank you ..this is great information. We dock at 7 and have to be back on the ship at 7. It sounds like it may easier going at our own pace. Is it easy to get a taxi from the port to these places?. There will be 4 of us and we could split the taxi to each. We also like to work in maybe a casual meal maybe with a view of an area. Any suggestions on the order we should do below? Also is there anything missing that we def should see?

The Acropolis:
Syntagma Square: Changing of the guards.
Panathenaic Stadium
Lycabettus Hill

Jolui is right. You really won’t be able to do all of those activities mentioned properly
If you have to be back at your ship at 1900 then you really only have time to do one or two things (maybe three) one your own
Was there in June second week - two nights in Athens, five in Hydra (Idra)
We went to the acropolis and Parthenon on second day, 1000 south entrance, not main entrance, no lines, wife booked tickets for family day before
You could easily spend 3-4 hours there, depending on your tolerance for crowds and heat!!
We grabbed overpriced sandwiches and drinks and walked to panathenaic stadium - it was closed there was an event later that evening
Went back to our hotel in syntagma through national gardens again rested then later that evening went to the acropolis museum and then had lovely dinner atop acropolis museum restaurant with excellent view of acropolis and Parthenon

Is it easy to get a taxi from the port to these places?

The taxi ride to the city center from the cruise terminal takes about 25 minutes depending on traffic.
There are taxis waiting at the terminal, but you can pre-book one, for example, with Welcome Pickups, a reliable service with licensed English-speaking drivers. He/she will be waiting for you with a sign with your name on it.
The cost is approximately €30.

https://www.welcomepickups.com/athens/

It would takes 3 days to visit Athens, just to see the basics. So, I'll just give you some information about the ones you mentioned.

The Acropolis:

If you want to avoid waiting in line to buy your tickets, it is essential to pre-book your ticket to the Acropolis by specifying a date and time slot. Read the access conditions carefully. Note that depending on the time of year the morning slots may become unavailable up to a week in advance.

Official website to purchase tickets:

https://hhticket.gr/tap_b2c_new/english/tap.exe?PM=P1P&place=000000002

There are two entrances to the Acropolis. If you take the side entrance, you'll be closer to Syntagma Square:

Side entrance location:

https://maps.app.goo.gl/ezGsUe46sZSxPd8t7

If you get a ticket to the Acropolis at 8:00 or 9:00, you can be out around 11:00 or noon.

Changing of the Guard

Every hour in front of the Parliament on Syntagma Square. The Sunday ceremony at 11:00 is a larger one.

Syntagma Square is about a 20-minute walk from the side entrance to the Acropolis.

The Panathenaic Stadium

The Stadium can be reached in a 15-minute walk from Syntagma Square, crossing the pleasant National Garden.

Directions:
https://maps.app.goo.gl/A1g3ufGybcL3n9XVA

There is little or no wait time to get there. You can request a free and good audio guide when purchasing your ticket.
Allow a 1-hour visit with the audio guide.

https://www.panathenaicstadium.gr/en/home/

Lycabettus Hill

https://www.lycabettushill.com/

Two options:

Take a taxi to the cable car station at the foot of the hill, located here:

https://maps.app.goo.gl/98wC6mrXVQVi2RKr5

or take a taxi directly to the top of the hill.

The Staduim from Syntagma Square: About 15 minutes by taxi (€10/€12) for both options.

There is also a bus option; I'll skip explaining it given the short time you have.

A map of Athens with the main sites and museums

https://www.google.com/maps/d/edit?mid=1OhGNGU1LUEgwFTul8u4YEe_tijF8Hqs&usp=sharing

You can do this on your own
With your ship docking at 0700 you can easily get to the acropolis south entrance by 1000
Take the free shuttle bus from where you dock to Piraeus metro station stop, 2 minutes walk from gate E8
Take metro line 3/blue line to syntagma square - 40 minutes
Syntagma square to acropolis south entrance 15-20 minutes - buy tickets online to skip queue of ticket buyers
Acropolis museum if you still have energy for more relics. But maybe lunch at the museum restaurant with a good view?
If you feel fortified after lunch maybe you can walk to the panathenaic stadium?
And then back to syntagma with plenty of time to get the metro to Piraeus port?

We walked. But take a taxi if the heat is too much

Unfortunately, gilbert_tagalog made a small mistake with the free shuttle bus to Piraeus Port, which he probably took from the ferry port and not from the cruise terminal.

This free shuttle bus doesn't go to the cruise terminals, and it would take you a 30-minute walk to get to the metro station.

However, there is the public bus 040 that can take you to Syntagma Square; the stop is right next to the cruise terminal. I didn't mention it because walking to the bus stop, waiting for the bus and taking it to Syntagma would take you almost 1 more than a taxi.

There is another bus line, the X80, but it doesn't operate before 8:30 a.m anyway.

Thank you all so much. We will be in Athens 1st week in Sept. How far in advance should we reserve tickets to Acropolis?. Or will it not be as hard to get them this time of year if waited till we arrive.
In summary of the feed back: If we took the private tour: taking the http://www.georgestaxi.com/ may be convenient in that we will see these stops; however not able to spend as much time at each. 250 euros split betwee 2 couples. If we decide to take the tour (pick us up at 8am) and instead of having the driver take us back to the port at the end we ask him to drop us off at Plaka (Or another area )around 1ish, would it take long to get a taxi back to our ship. We would like to be back on the ship by 5 or 6 pm.
Is Plaka an area worth seeing? Eat lunch then head back to ship via taxi.
Still weighing the option of going on our own too.

Currently, checking the website, all morning slots for the Acropolis are booked up about a week in advance. But it's like the weather forecast, impossible to know in advance which time slots will be unavailable in September.

George's Taxi will only drive you from one place to another; it's just a private driver with a predetermined route. I don't know if you can change it, and if so, what the possible additional costs are.

What's certain is that the driver won't go with you to the sites you want to visit, and any other taxi driver in Athens could take you from point A to point B, just like George's Taxi does (not to mention the metro and buses).

There are at least 20 million visitors to Athens each year who wander the streets and explore the city without needing a driver, be it George's Taxi or whatever.

Why shouldn't you be able to do the same?

But the choice is yours.

I suggest some reading while you wait for September:

https://www.thisisathens.org/

Jolui, true
I meant cruise terminal shuttles and port of Piraeus authority shuttle - both free
From terminal A/gate11 you can get to gate E8 and then to the metro stop

gilbert_tagalog, From what you're describing, I think you took either a complimentary shuttle specifically chartered by the cruise line, or an OASA public bus without knowing you had to pay for a ticket.
There are indeed public buses that stop at Terminal A/Gate 11 and also at other ferry port gates, from where you can take the free shuttle to the subway station, which is right in front of Gate E5.

Anyway, these options take time and, in my opinion, are not compatible with what bhgambill wants to do.

But If you have a reliable source mentioning this free shuttle from Terminal A, please let us know, it might be of interest to other travelers.