We may be cheating it a bit with including this one. You can't actually visit this island unless you belong to the Elliðaey Hunter Association.
However, you'll be able to spot it and take plenty of photos from the ferry in to and out of Vestmannaeyjar. You can also spot it from the island itself and we found that when you clim all the way up to Eldfell volcano you get a fantastic view of the island with its idyllic lodge as well. Some things just look better from a distance anyway :)
There are excursions that take you around the island by boat, and some may even offer you to actually do get on the island. But these trips don't happen very often.