Krujë (32km north, around 40 minutes) is the most rewarding short trip. The hilltop town was the stronghold of Gjergj Kastrioti (Skanderbeg), Albania's national hero, who held off the Ottoman army here in the 15th century. The castle houses the Skanderbeg Museum. The old bazaar below is one of the best-preserved Ottoman bazaars in the Balkans — good for handmade crafts, copperware, and antiques.
Durrës (38km west, around 40 minutes by motorway) has a 2nd-century Roman amphitheatre — the largest in the Balkans — partly buried beneath later buildings. The Byzantine forum walls and a good archaeological museum are nearby. The city also has a long beach and is Albania's main port.
Berat (125km south, around 2 hours) is a UNESCO World Heritage Site — a well-preserved Ottoman town with whitewashed houses climbing a hillside, a Byzantine castle on top, and several notable churches. A full day trip.