Yeah, there are many marked trails in the area that you can easily follow for some really good hikes. The most famous is the Fimmvörđuháls, about 22km between Skógar and Thórsmörk that are usually covered in 2 days. Another popular route is between Landmannalaugar and Thórsmörk.
The view you see in the picture is from one of the secondary trails around Thórsmörk.
Keep in mind that the area is very popular with hickers from all over the world, so you'd better book accommodation in advance, especially for huts along the treks. If you prefer to trek far from the crowds, I suggest you go to Hornstrandir instead. That's the icelandic "final frontier"