For sheer spectacle, it's very hard to beat Jökulsárglújfur National Park, which combines great hiking trails, a breathtaking canyon and Dettifoss, the largest waterfall in Europe. You can get there on day tours from Akureyri.
The classic long hike through Iceland's interior, Laugavegurinn is a five-day walking route taking you from the bathing springs at Landmannlaugar, deep in Iceland's interior, to the gorgeous Thorsmörk national park, nestled between glaciers in South Iceland. Even if you don't want to walk the whole thing, you can see the highlights on bus tours from Reykjavík to both Landmannlaugar and Thorsmörk.
If you're not a hard-core hiker, relatively short walks around Myvatn reveal all sorts of amazing sites. They've got an entire park (Dimmuborgir) of bizarre lava formations, flocks of birds, craters, and a low mountain you can climb.