Athens: Acropolis (UNESCO) and Dionysos Amphitheatre, Monistiraki Flea market, National Archaeological Museum, Varvakios Agora (central market, plan much at Oinomageireio taverna), Syntagma square change of guard in front of the Hellenic Parliament (every day at 11 in the morning, but Sunday a more complex ceremony takes place),Museum of Music Instruments, Hadrian'sLibrary, Church of Panagia Kapnikarea, War Museum, National Gallery of Greece (plan plenty of time), Runner Glass Sculpture right in front of the Gallery on the square, Lykeion Archaeological site, Byzantine and Christian Museum, Cyclades and Benaki Museums, Keramaeikos cemetery, Museum of Islamic Art in the same area, you can walk from the ancient cemetery. Dinner places to recommend Paras Taverna and Kotili with Greek music and dance.
Archaeological Museum.
Thessaloniki (UNESCO) Rotunda, Church of Saint Demetrius, White Tower
Excursion to Mt. Athos (open only to male pilgrims, accessible by boat only from Ouranoupoli to Dafni) with prior permission from the Pilgrim's office. The best experience is to stay overnight in one of the monasteries, reservatiion recommended.
Mykonos and its loud music bars and party beaches, Little Venice place, excursion to Ancient Delos (UNESCO), a great archaeological site, by boat from Mykonos.
Santorini that will take your breath away with its great view over the cliffs, excursion to Ancient Akrotiri and the colored beaches in the south.
Crete's natural beauty is a hidden gem, plus the Palace of Knossos, the Archaeological Museum of Iraklio, amazing Rethymno and a sidetrip to Moni Arkadiou. Chania has a very pittoresque Venetian quarter, fortifications, old townhouses and a lighthouse.
Rhodes Old town (UNESCO) with its cobbled streets and history, not to miss the picture perfect town of Lindos. Symi's Gialos one of the prettiest harbours in the country, with an Italian vibe.
Patmos with the Greek Orthodox pilgrimage monastery of Saint John the Theologian, the Apocalypse Cave, plus Kambos beach.
Corfu, a nice mix of Venetian fortresses and beaches. Great monasteries atop the rocks in Meteora (UNESCO), one of the finest sights in whole of Greece.
In the Northwestern corner I can recommend Kastoria with its pretty location on Lake Orestiada, the Prepsa lakes on the Albanian border, Konitsa, Papingo and the whole of Vikos Aoös National Park and that includes North Pindus that has been added to the UNESCO list in 2023. Gefiri Placid bridge, Voidomatis bridge, lots of pretty stone pedestrian bridges in the area. Dodona amphitheatre.