St Augustine (NE Florida) is very dog friendly! Many hotel/motels accept dogs and most restaurants with an outdoor seating area allow dogs. Dogs are allowed on the beaches -leashes are required during certain times but you can almost always find a quiet area where no one will care if dogs aren't leashed. You can also drive a vehicle onto the beach (i know, it sounds odd, but it is very cool) so you can bring all your stuff and unload in a secluded spot.