If you're interested in discovering the forces of nature and the history of the area, pick up the booklet Klaustur trail (600kr), which outlines a 20km walking trail that circles the village and takes in many of its natural features. There's also Hiking Trails In and Around Kirkjubæjarklaustur (750kr). Maps and good info are available from the Skaftárstofa visitor centre.
There are a number of in-demand accommodation options (most with on-site dining) in town, and in the beautiful rural landscapes around Klaustur. You'll need to book well ahead to snare a room in the summer; prices generally do not represent good value.
Winter openings are always worth confirming.
Most travellers dine at their accommodation, and that's no bad thing – there are not a lot of other options in Klaustur, and in-house restaurants are quite good (most are open to nonguests, too). If you're looking for a higher-end experience, head to the Icelandair hotel's restaurant.
Look out for local Arctic char (trout) on menus – it comes from pure water directly under the nearby lava field.
Drinking & Nightlife
Aside from a quiet drink at your accommodation, the only option is to visit Systrakaffi.