At the pier of the city harbor, there is a small observation tower with a beautiful view over the city and the harbor, out into the strait of the Strait of San Juan de Fuca and the mountains in the hinterland around the Hurricane Ridge - if the view allows it and it does not hazy. Otherwise simply enjoy the maritime atmosphere and watch the ferry from Canada arrive.
In Port Angeles, some companies offer whale watching tours. Great care is taken not to get too close to the animals. These tours can also be booked online. A walk along the pier and the coast is worthwhile.