The top image is the Point Wilson Lighthouse at Fort Worden State Park in Port Townsend, WA. The angle makes it look less like a point. The main body of Puget Sound (Admiralty Inlet) is just on the other side of the lighthouse. The hillside in the distance is on Whidbey Island.
Point Hudson is at the NE corner of Port Townsend, right at the end of Water Street. This was taken from up on the hill at Fort Worden just prior to the image above. You can walk the beach from one point to the other … just make sure to check the tide charts before you start!