Some suggestions for a short drive:
* Beaches of Kalamaki, Matala, Komos and Kokinos Pirgos

* Archaeological sites of Phaestos, Gortys, Agia Triada, Matala and Komos
* Gypsy market in Mires (Saturday) and Tympaki (Friday)

Some places reachable within 1 hour:
* Via Listaros (Monastery of Odigitrias) to Kali Limenes
* Via Kouses and Pombia to Lendas
* a beautiful tour along the mountain villages Zaros (trout farm, Rouvas Gorge and the monastery of Vrondisiou) Vorizia, Kamares, Magarikari, Vori (anthropological museum) and Klima
* Agia Galini, where boat trips are also possible to e.g. the "Paximades islands" 

And for when a longer time in the car will be no problem:
* Heraklion & Knossos (ca. 1¼ hours)

* Rethymnon (approx. 1½ hours)
* Chania (approx. 2½ hours); the most beautiful city of the island
* The beautiful Palm forest of Preveli (approx. 1½ hours)
* Plakias (approx. 2 hours)
* Frangokastello (approx. 2¼ hour)
* Chora Sfakion (approx. 2½ hours)
* Arkadi Monastery (approx. 3 hours) drive through the Amari valley on the old Rethymnon road. Visit the Byzantine church in Thronos on the way.