Fort Worden is a very nice park and yes you are near the beach. A lot of history there and even a movie backdrop (An Officer and Gentleman was filmed there). Also a short drive to Port Townsend for shopping.
Fort Worden is our favorite place to camp! There are lots of places to explore, just at the park. There are two museums (Commanding Officer's Quarters and the Coast Artillery Museum), lots of trails, bunkers on top of the hill above the park, a Marine Science Center, lighthouse, and great beaches. There are great neighborhoods around Port Townsend and the town has unique shops and lots of great places to eat. It's a very friendly place. Have fun!