>>1822313For the most part Key + Olympic peninsulas are far less populated so they are generally a better experience. Unfortunately a lot of beautiful trails are not dog friendly.
A good reference is washington trails association website wta dot org which has a hiking map you can filter by 'dog friendly' and will provide good information. Basically you'll be going to the east side of Olympic national park, and taking a cut out from highway 101 at some point.
Hikes of varying difficulties I would recommend:
Green Mtn./Wildcat trail - this is a pretty rough hike but it's beautiful
Cape Flattery - out past Neah bay on NW most tip of peninsula, long drive but it's pretty amazing. Literally hundreds of eagles
Deception Pass - if you can take a ferry to Whidbey Island it's in the middle. Small trail but a very cool place imho
Blake Island - either have to take a boat or pay for the service from Seattle. Has an expensive dinner/dance show that is unique, but again is really pricey. Great hike around the island though, good views of Puget Sound/Seattle
Point Defiance - North Tacoma, good park that looks over a lot of water, despite being next to a major city.
Fort Ward - South of Poulsbo off 305. Not much of a hike but a neat area. Sometimes you see a bit of graffiti though which is very disappointing.
Newberry Hill - S of Silverdale, long hike. Not my favorite but should be dog friendly.
Outside of that my favorites are either not dog friendly or require a lot of driving to get over by Rainier, cascades, etc. I highly recommend going to Paradise (Mt. Rainier) late July / early August as the alpine wildflowers come out and it's spectacular. VERY BUSY. Ass loads of tourists who can barely make it up the first 100 feet, but it's just amazing up there. Hasn't been ruined by wildfires yet either. They don't get wildfires up there but the typical ones from Canada just billow smoke down across the entire state and make it pretty rough walking out there.