The Inn at Langley is a terrific B&B located in a neat little town on Puget Sound not too far from Seattle. (It's not on the coast I know but it is seaside) Not sure what the pet policiy but it's worth calling them to find out.
Alternatively, you could head up to Port Townsend where there is a plethora of B&Bs from which to choose. Great beach combing etc. there too.
You can't go wrong with either town and I'd start with the one closer in. Good luck!