Hotels in Greece

For Athens - we stayed at Athens Gate Hotel. They have a great buffet breakfast and amazing views of the Acropolis. I can't speak to whether they have rooms for 4 people or not. There were just 2 of us. We walked to the Acropolis from our hotel and the hotel is right by the Plaka area - great for shopping and restaurants. We walked all over Athens. Enjoy your trip.

If you can be a bit flexible on your arrangements? Two adults in one bed, 1 child/grandchild in a single for each room, then you could book the standard double with extra bed at the Acropolis View Hotel in Athens for 158 euros a night per room in July. Your chances of finding two rooms with 3 people each in them improve your chances of finding a room.

This hotel is well located and has had good reviews here on the forum.

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

Have you considered staying in apartments or houses and not only in a hotel?

In the Greek islands there are 2 to 3 times more than hotels, often managed by locals and sometimes with a breakfast service.

My main comment is why are you thinking of staying in not so nice Heraklion instead of in charming Chania?
Chania is considered one of the two prettiest towns in Greece; the other is Napflio in the Peloponnesean peninsula.
Hotels in Chania; Porto Veneziano, Kriti Hotel , Kydon. Check Air BnB too.
Hotel in Athens; New Hotel
Why travel all that way to Rhodes for only one night; it's a nice town but not near Athens like the Cyclades Islands are. Look at Paros or Naxos for a nice, closer island stay.Nice islands for families with children. You can take a ferry from Crete more easily to the Cycladic islands too. We only visited Rhodes when we were traveling on the Turkish coast.

And I’m wondering if you’ve looked into transportation between Crete & Rhodes? It’s an 11-14 hour ferry trip, or else a flight back to Athens & then a flight to Rhodes. For one night it would make no sense.

A better plan would be to fly directly to Crete upon arriving in Athens, stay in Crete 4-5 nights, then fly back to Athens for 1-2 nights. You should be in Athens the night before your flight home, and you want to keep all of your Athens time together to avoid multiple trips to the airport & hotel checkins.