Here is a map of the South-East part of Iceland with the places described on the page marked by red dot.
Distance from Reykjavik to following places is:
Vík: 190 km - Kirkjubæjarklaustur: 260 km - Skaftafell: 330 km - Jökulsárlón: 400 km - Höfn: 475 km - Djúpivogur: 570 km.
Family Travel in South East Iceland
Travelling in the south-east part of Iceland
1. Vík and Kirkjubæjarklaustur
Two small villages are on the way along the east coast. One is 'Vík', where you have to go down to the beach and take a look at 'Reynisdrangar'. Be careful by the sea, the waves are very strong so look close after your kids.
Further is Kirkjubæjarklaustur with a very friendly atmosphere. It is nice stopping there and walking up to the hill the village is under. It is not far and you get a very nice view. You may also find a nice little waterfall, 'Systrafoss' on your way.
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.
3. Höfn in Hornafjörður
The main city in the eastern part of Iceland is Hofn in Hornafjordur. The view from Hofn is incredible with the biggest glacier in Iceland, Vatnajökull, close by. It is possible to take trips to the glacier. Please check this website.
On the way to Höfn you pass 'Jökulsárlón', glacial lagoon which is worth stopping by. You can sail between the icebergs on a boat in special trips, see here.