The Makah Museum, formally the Makah Cultural and Research Center, is the place that keeps Neah Bay from being just a scenic road-end. Its core collection includes hundreds-of-years-old artefacts from the Ozette Archaeological Site, along with historic and contemporary material related to Makah life.
Check current opening status before you go, because tribal public-health and access rules can change. If it is open, make it your first stop; the beaches and headlands make more sense after you have some cultural context.