The area around Hólmur is well suitable for walking. The birdlife is diverse and depending on the season you can see wild animals, such as reindeer, wandering around.

A trail to the glacier Fláajökull lays in the north of the farm and can be both walked or driven. In the south and west of Hólmur you will find moorland.
Multiple hikes can be done in the neighborhood: Hiking map of the area pdf

33 km to the east is the fishing town Höfn, with a gas station, supermarket, swimming pool, golf course, and museums.

Hólmur is in a good day – trip distance for sightseeing
Skaftafell national park – 100 km away
Ingólfshöfði nature reserve – 120 km away
Djúpivogur, a peaceful fishing village – 100 km away

Activities in the area include:
Natural hot tubs: Hoffell

Glacier trips – hikes, jeep tours, ice climbing, snowmobile etc: https://glacieradventure.is/
https://www.iceguide.is
http://www.glacierjeeps.is
https://glacierjourney.is
https://localguide.is/

Boat trips on the glacier lagoons:
https://fjallsarlon.is/
https://icelagoon.is/
https://www.glacierguides.is/jokulsarlon-glacier-lagoon
https://www.iceguide.is/tours/glacier-kayak-adventure/