Not long from city limits you will find Elliðaárdalur Valley, which is a lush recreational area popular for walkers and cyclists alike.
Also, beautiful fishing rivers in the surroundings here, and fishing is allowed here, but of course only with fishing license card.
One of the most popular fish to catch here for fishing fans is the Salmon.
Ask in tourist office for license possibilities. Note it's also possible to fish in the nearby Elliðavatn Lake and Reynisvatn Lake.