Begin your search for a cheap car rental near Eldfell & Helgafell by entering your travel dates and pick-up and drop-off points. That’s how economical a car rental can be around this well-known attraction, but there are a few things that’ll influence how much you pay — your travel dates are just the start. Whatever your budget and desired car type, Expedia has awesome offers from a range of car rental companies that’ll get you on the road for less.