You can't go to the Faroe Islands without taking a boat trip out to the famous Bird Cliffs.
Puffins are the most common bird seen, although sometimes some others make an appearance as well.
Go to Vestmanna and get a ticket for one of the several boat tours they run each day. The boat is comfortable and has a nice, warm, below deck area where you can still see the islands without having to be out in the cold and wind (or rain).
It will take up your morning, but it's worth it.