Written

there is clear evidence that some cities (particularly Athens) remained under Byzantine control

though by A.D. 620 Emperor Heraclius withdrew all Byzantine troops from the Balkans, his son and successor, Constans II, began attacking the Slavs, first in the hinterland of Constantinople (656/7, Theophanes, Elias of Nisibis, Agapios of Manbij)
in 662/3, on his way to Syracuse in Sicily, Constans spent the winter in Athens (Liber Pontificalis, Paul the Deacon)
694 is the earliest date mentioned in a series of Athenian bishops mentioned in graffiti on a column of the Parthenon
Empress Irene (790, 797-802) was from a noble family from Athens (Theophanes)
at the Sixth Ecumenical Council in Constantinople (680-1) were present the bishops of Thessalonica, Corinth, Argos, and Lacedaemona (Mansi 11:189-90)
at the Quinisext Council (in Trullo)(692) were present the bishops of Thessalonica, Edessa, Amphipolis, Philippi, Ainos (Mansi 11:921-2)
at the Council of Nicaea in 787 were present the metropolitans of Corinth and Athens, and the bishops of Nikopolis (in Epirus) and Patras (in Peloponnese)
at the Photian Council of 879, Greece is represented by 12 metropolitans and bishops

despite contraction and destruction, Athens remained a center for education and study

St. Ghislenus, who died in Hainault (Belgium), was an Athenian by birth; he tells us that he studied philosophy in Athens as a young man, ca. 650
Theodore of Tarsus, who became archbishop of Canterbury (668-90), had studied in Athens, according to a letter of Pope Zacharias to Boniface
Stephen of Surozh, future bishop of Sogdaia, made a pilgrimage to Athens in the mid-700s, and conversed with rhetoricians and philosophers (Greek Synaxarion, 73)

eastern Greece seems to have been organized very early as a theme

a general of an eastern theme, Leontius, was appointed general of Hellas in 695 (Theophanes)
the theme of Hellas revolted in 725/6 against the iconoclastic emperor Leo III, and sent a large fleet under the command of an officer called Agallianos (Theophanes)
by 755, Hellas was a populated region, for Emperor Constantine V decided to move families from there to Constantinople, to help re-populate the city devastated by the plague of 746 (Theophanes)

BUT: there is also evidence that Slavic tribes have already settled northern Greece

three Slavic tribes (Rynchines, Sagudates, and Drugubites) besieged Thessalonica in 677; at that time, a fourth tribe, the Belegezites, lived in Thessaly and produced grain in sufficient quantities to provide supplies for the besieged city (Miracles of St. Demetrius)
by that time, there were numerous Slavic pirates in the Sea of Marmara, reaching as close to Constantinople as the island of Proconnesus
annoyed by the turbulent tribes near Thessalonica, Emperor Constantine IV organized an expedition against them in 678

there were also Slavs and Avars in central and southern Greece

when in 723 bishop Willibald of Eichstatt traveled from Syracuse to Constantinople, he stopped at Monemvasia, at the southernmost tip of Peloponnese; he called the place "the Slavic land" (MGH SS 15:93)
perhaps in the 730s a Byzantine warlord from Taormina (Sicily) organized an expedition across the sea; he took a number of prisoners from among the Avars living in the province of Athens (Life of St. Pancratius)

782/3: the first attempt to subdue the Slavic tribes in central and southern Greece (Theophanes):

an army under the logothete "tou dromou" (of the Swift Course), Staurakios, advanced to Thessalonica and Hellas, where he subdued the Slavs and made them pay the tribute to the emperor
he then moved into Peloponnese and took many captives
around 800: a new theme was created in Peloponnese

880: Byzantine troops recruited from among the Slavs fight against the Arabs in Sicily