Heimaey is a rather small island, only 7x4 km, so everything is within walking distance. There are hiking paths all over the island so any reasonably fit traveler should be able to enjoy the sightseeing on foot.
Cars can be hired at the airport or in the town. Prices start from about 8.000 ISK a day.
Guided bus tours, boat tours and hiking tours around the islands are also available. Information on these tours can be found at VÃking Tours and EyjaferÃ°ir.