In 2000, I journeyed to Greece for the first time and it was a magical experience for someone who grew up loving mythology and who took Ancient Greek for her high school language requirement. I loved the food and the architecture and declared that I'd be happy to come back any time. In the quarter century since, I've gone back several times and discovered that I could enjoy many other things in that country.
Santorini
If you look up this island, you will recognize the iconic blue roofs and white structures. The various settlements are gorgeous and there is a handy tram from the port to the top of the cliffs. You can shop, dine, take gorgeous pictures, or just enjoy the sunshine.
Along the narrow streets, you can find many stores, selling anything from fashion to ouzo. Around one bend, you can find a small cinema that is only open during the summer and plays Mamma Mia and My Big Fat Greek Wedding. For me, the most enjoyable part of my visit to Santorini was eschewing the tram and navigating around donkeys to walk all the way down to the port.
Rhodes
This is one of my most personal recommendations and needs some context. I regularly travel with the same friend and we decided several vacations ago to each choose one tour or experience that we can't miss. This has led to fast-paced adventures in Tuscany or a German-Spanish tour of the Alhambra in Spain. On our last visit to Greece, a religious tour of Rhodes caught my eye and I claimed it as my must-see experience of the trip.
Our tour guide walked us through the city that shares its name with the island and we enjoyed learning more about the various churches, but the best was at the end of the tour. In one plaza, I saw a memorial written in Greek and Hebrew and discreetly asked to know about the Jewish history of the island. She instructed me to keep up with her when we reached the Kahal Shalom Synagogue.
Next to the oldest Jewish synagogue in Greece is the Ebraiko Mouseio tes Rodou (Jewish Museum of Rhodes) and both sites are well worth the visit. The Museum chronicles the enduring legacy of the Jewish community in the face of astounding hardships. There are places within the synagogue that bear testament to how the Jews of Rhodes were impacted by the deportations in World War II. Rhodes is a place of wonderful history and culture, but understanding more layers of its history is a profoundly moving experience.
Delphi
This is the place I would recommend bringing adventurers across a variety of ages. For those who aren't interested in reading signs about the remains of temples, Delphi is a great place to explore the outdoors. For those who need more than fresh air to enjoy a site, it is steeped in history.
Read the signs by all means while hiking among the ruins, but for a really fun time, read a few of the anecdotal tales about messages received by the Oracle at Delphi. The Temple of Apollo was home to a priestess who would give famously ambiguous statements. Check out any of the 500 prophecies attributed to Pythia.
Epidauros
On that first trip to Greece, I took a tour of the Peloponnese and the undisputed gem of that tour was Ancient Epidauros. It is hard to avoid a sense of overwhelming awe when standing anywhere in the amphitheaters, which are in remarkably good shape. The archaeological museum is a must-see for art and history fans. Next to the Ancient Theatre is the Sanctuary of Asclepius, a famous healing center. And the stadium was the site of athletic games every four years.
While there are family-friendly tours at Epidauros, the Kids Love Greece website also mentions that it is also within driving distance of other kid-friendly destinations. Visit Corinth and its canals or see the Lion's Gate at Mycenae.
Greece has something new to discover with each visit and can accommodate many interests or needs. Hope this has given you a few new ideas.