ἡ γὰρ ἀκρόπολις τὸ πάλαι τῶν Ἀθηναίων ῥηχῷ ἐπέφρακτο
Long ago, the acropolis of the Athenians was fenced in by a palisade.
The accusative signals a point in time as a satellite.
This mainly concerns fixed expressions: τὸ νῦν ‘now’, τὸ πάλαι ‘long ago’, πρότερον ‘before’, τὸ πρότερον ‘the previous time’, πρῶτον ‘first’, τὸ κατ᾽ ἀρχάς ‘in the beginning’, τὸ πρῶτον ‘in the first place’, τὸ τελευταῖον ‘finally’, τὸ λοιπόν ‘in future’, ἀκμήν ‘just in time’, καιρόν ‘in season, just in time’, τὸ δεύτερον ‘secondly’ (but ἔπειτα or ἔπειτα δέ is more usual in a list).
The accusative marks when or at which moment something happens in a succession of events; the use of the dative of place is much freer.
ὁ δὲ διώξας τὰς μὲν συλλαβὼν ἐπὶ τὸν Ἑλλήσποντον ἤγαγεν, αἱ δὲ ἀπολειφθεῖσαι τὸ λοιπὸν ἦσαν ἄγριαι
(Hercules) pursued (the cattle of Geryon), caught some and drove them to the Hellespont; but the remainder were wild from then on.
καιρὸν δ’ ἐφήκεις· πάντα γὰρ τά τ’ οὖν πάρος | τά τ’ εἰσέπειτα σῇ κυβερνῶμαι χερί
You arrive just in time; for all that I have done in the past and shall do in the future is guided by your hand.