Advice for Late July-early August Trip

Consider carefully if you will be on your game for a nearly three-hour drive after an overnight flight (assuming you are flying in from US unless that is a missing piece of info).
Driving in and out of Athens is going to be hectic to say the least, so please share where you are staying and add if you have driven in a large unfamiliar city like this before.
Your day trips are pretty long--I know you are trying to work around some complications, but this is concerning to me. I think you would be better off with day tours. If you do that, then you could fly to an island after the competition. If you don;'t, then you could drive to the Peloponnese after the competition. You could spend those early days touring Athens and doing day trips.
Rental car on ferry is up to the car provider so you have to check with them.

I completely agree with valadelphia.

You'll be arriving, I presume, after a long transatlantic flight, and driving to Delphi in these conditions is not only unreasonable but also dangerous for you and others. Especially since it will be a Friday at the end of July, when Athenians leave Athens for their August vacation. No need to add your inexperience with driving in Greece to the traffic jams.

So, slow down. Stay in Athens when you arrive on Friday.

In Athens in August, it's possible, even probable, that temperatures will reach at least 40°C (105°F) or even 45°C, forcing archaeological sites to close from 11 a.m. to 5 p.m. for safety reasons. These days, the temperature is around 38°C during the day and doesn't drop below 29°C at night. So, even if you're open to activities, I guarantee you'll want to slow down.

If this is the sport I think it is (but I could be wrong), the events aren't taking place in the center of Athens, but a 30-minute drive from the center and far from any metro station or bus line that would connect to the city center. Have you planned how you'll get there?

Regarding the period from July 31st to August 5th, it's only 5 days.

Option (a): Peloponnese can be a good choice provided you don't want to visit the entire Peloponnese.

Option (b): Cyclades, 5 days is barely enough to visit one island. If you like crowds, choose Paros or Naxos. Otherwise, Sifnos can be less crowded. Also, see Serifos or Tinos.

Option c: The Ionian Islands will require you to take a flight, at least to Kefalonia since Lefkada doesn't have an airport. Is this really necessary with the limited time you have? In my opinion, no. These islands, at the western end, are almost closer to Italy than Greece.

We did, as you are considering. Drove directly to Delphi on arrival to Athens. Spent a lovely night there, visited the Delphi site in the morning and drove on to Meteora for two nights. Worked great for us. From there, drove to Pireaus and took the ferry to Sifnos. Loved Sifnos.

Have a great trip!

Thanks for the feedback!

1. We'll have an apartment in either Koukaki or Plaka from July 25th-31. We'll stay there on the July 25th & 26th, then head for adventure or the 27th and 28th to Delphi, Corinth, or Napflio then.

2. JoLui, you probably picked the sport. It's UWW U17 wrestling at the Ana Liosia Olympic Center. We're planning to drive there and back from our accommodations in central Athens on the Tues/Wed. 29th and 30th (competition is from 10AM - 7PM). Is that reasonable or a bad idea stay outside of the city center?

3. On the 31st or we'll travel to an island - Cyclades it is. Keeping in mind that we'll have a 15 and 17 year old, we want to be on an island with enough for them to remain entertained. Would that impact your recommendation for an island (we don't mind moderate crowds, but not Santorini in August level).

Thanks so much for all of the insight!

When we took our kids to Naxos they both loved it there. A good town beach just a 10 minute stroll along the headland to St George beach to the delightful main town with a waterfront promenade and a maze of back alleys leading to a Venetian era Kastro at the top.
Some images
Naxos town 2024 https://www.flickr.com/photos/stanbr54/albums/72177720318203165/

Until the morning of the 29th, whether you stay in Plaka or Koukaki, you won't need a car to visit Athens.

• Koukaki is a quieter neighborhood than Plaka, less crowded with tourists, but very lively with local life, quite a few bars, restaurants, and shops (we're regulars there even when we're not staying in this neighborhood).

The eastern end of Koukaki is bordered by Syggrou Avenue, which is where all the car rental companies are located. So on the morning of the 29th, you could pick up your rental car at one of these offices. It will only take a 5-minute walk. In Koukaki, there are mostly short-term rentals (Airbnbs) which are more suitable for the number of days you're staying in Athens.

Koukaki is this area (just south of Plaka)

https://maps.app.goo.gl/PmPd8GmyAY46DhQ17

The nearby area on Syggrou Av where all the car rental agencies are located (zoom in to see more)

https://maps.app.goo.gl/uy6XK9mT3bjEd2Df7

With a car, you could also take a day trip to the beautiful Kaisariani Monastery, which is 20 minutes from the center of Athens and overlooks the city from above.

https://maps.app.goo.gl/ZEuSs5mBfpLwecXV7

You could even take a day trip to Cape Sounion.

https://maps.app.goo.gl/M7mQiUg7UJFmiCn56

(We visited both on the same day)

For your information, if your son is staying at the President Hotel, as planned by the organizers, there are two bus lines, the 550 and the 10, which connect Koukaki from Syggrou Avenue to this hotel. In Koukaki, the bus stops are a few meters from the Syggrou Fix metro station; they stop at the "Zerba" bus stop, a few meters from the President Hotel.

You might have trouble parking on the street, especially in Plaka, where there are only tiny streets with no parking available. It's easier in Koukaki. There are some paid parking lots. Expect to pay around €25 for overnight parking.

As for which island to go, I prefer to let you decide.

Personally, the crowds in Naxos Town and its surrounding beaches in August are a real nightmare for me. I couldn't stay there for more than half a day, but I admit that my tolerance threshold for crowds is quickly reached.
It's up to you...

Sounds very busy!!
We were in hydra recently for five days
Our son was doing off season training for his university XC team and our daughter in high school was busy doing her internship work for NASA - all in the morning on their own
In the afternoon we caught the beach boats to Bisti beach - 1100, 1200, or 1300 departures, returning 1630 or 1800
Just relaxing for five days on an island with no cars
Good luck to your son!!