James,
The weather will be wetter than you are probably used to in Florida. The climate is mild, and the islands are a bit of a banana belt in general. I lived on the very south end of the island for a time and liked the small town atmosphere as well as the beautiful scenery of the island itself and of Puget Sound. You will be stationed up at the north end of the island at Oak Harbor, which has access to the mainland nearby via a bridge, as opposed to the ferry that services the south end of the island. The pacific northwest is a gardener's paradise with its mild coastal climate and ample precipitation. If you're craving some dry heat, you can head across the Cascade Mountains to the dry side of the state in the summer time. (We have lots of snow over here in the winter so you probably won't want to venture over in those months.)
I don't know much about the area around the navy base, but the people on the island are friendly and outgoing. Boating is fun and you should take the opportunity to explore the San Juan Islands, if you get a chance. Best of luck to you in your big move!