2. Skaftafell National Park and Vatnajökull

Skaftafell national park was established in 1967. It includes a considerable part of Glacier Vatnajokull and the Laki Area, ideal for hikers. There are no roads in the park, but a lot of trails for all kinds of hikes. Try for example to walk up to the glacier-edge, about 1 hours walk easy for everybody. On the way you see marks showing where the glacier-edge was some years ago, showing how much the glaciers are pulling back.
In the park there are camping grounds (nice to have picknic or barbique), toilets, washing machines, a restaurant, a small shop and a very interesting Visitors Centre. There are also regular guided walking tours and tours from the park to the volcanic Laki area.
Vatnajökull glacier is the biggest glacier in Iceland. I would recommend guided tour to all glaciers as they are ever changing and you have to know them well to be able to travel safe there. Check for example this web-site or this one.