Skomvær is small enough that "things to do" really means three things: walk the island, watch the birds, and look at the lighthouse. None of them take long, but the place rewards anyone who has gone to the considerable trouble of getting here.
The single human-made attraction is the Skomvær Lighthouse, automated since 2005 but still standing — the southernmost lighthouse of the Lofoten chain and the last navigation light before the open sea. The natural ones are the seabird colonies ringing the cliffs and the bare-grass meadows in the island's interior, both at their busiest in early summer.