Great hike to see amazing views of the island. It starts just behind the the playground in Herjólfsdalur Valley. It takes about 20-30 minutes to get to the ridge. From there you can go left if you aren't afraid of heights and continue up the mountain. However it does get very steep on both sides so this is not for the faint of heart.

Or you can go right and continue around the crater top and even over the side to Kliff and Heimaklettur