I always loved camping at fisherman's memorial campground in Narragansett, RI. Spent a week there every summer as a kid. Bike/walk to Point Judith and Galilee. Salty brine beach is very close.
You could check out Scussett Beach or Bourne Scenic Park under the Bourne Bridge. Scussett has the beach on cape cod bay and the camp ground has the pond. Not sure about dogs.