Pick a passage of a Latin or Greek text and memorize it in Latin or Greek. Memorizing the opening of epics is traditional: Homer's Iliad and Odyssey for Greek and Vergil's Aeneid and Ovid's Metamorphoses for Latin. Or choose a passages that's particularly meaningful to you. Also good are any passages from the Greek New Testament or the Latin Vulgate.
Links to online texts:
Homer's Iliad and Odyssey
Vergil's Aeneid
Ovid's Metamorphoses
Greek New Testament
Latin Vulgate
