We recently decided to explore Potlatch State Park on Hood Canal. While the park does have plenty of campsites if you're interested in camping, this is the place to go for clamming, crabbing and oyster harvesting. You can even catch shrimp! There are limits to the amount you can take, and you must have the proper license, so be prepared before you head out here.
There are rocky beaches and sandy beaches; I'd call this a shell-y beach. Our toddlers loved walking around and picking up all the shells lying around. We'd thought about bringing our dog with us and in the end decided not to--I'm glad we didn't because I think all those shells would've shredded her poor puppy paws.
Even though the day-use area where we were was pretty small, we spent a couple of hours just hanging out and tossing empty shells into the water. It was beautiful and peaceful, especially when we first got there mid-morning and mist was hovering over the water.