Argassi is about 5 km south of Zakynthos Town and roughly 7 km from Zakynthos International Airport. Taxis are the simplest way in, especially with luggage; the ride from the port or airport is short and usually inexpensive by island standards.
Local buses run between Zakynthos Town and the southeast coast in season, but service is thin outside summer. If you plan to visit beaches beyond the resort strip, rent a car or scooter for at least a day.