The North East part of Iceland is incredibly intact area in terms of wildlife and nature. Any kind of outdoor activity, is highly recommended to experience what nature has to offer.
Raindeers are living in the mountains of North East Iceland, and tours can be provided to see them during breeding time (Sept/Oct). Wild birdlife can be explored, even in the hotel area.
Reccomeded webpages;
http://www.visitegilsstadir.is/en/things-to-do
http://www.visitegilsstadir.is/static/files/perlur2017_netversion.pdf
https://www.borgarfjordureystri.is/home
Puffins live in summer