One of the most lush and beautiful areas in the entire country is on the Olympic Peninsula.
The virgin forests of the Quinalt and Hoh Rain Forest have some of the most diverse ecosystems on the planet.
It is incredible, but very unlike the rain forests of Costa Rica and the Amazon.
Native species include Pacific Tree Frogs, Northern Spotted Owls, Bobcat, Cougar, Raccoon, Black bear, Roosevelt elk, and Black-tailed deer.
The North Olympic Peninsula area is an absolute wonderland if you enjoy the outdoors. I'd suggest basing yourself in either the Sol Duc campground or the Elwha campground. Each has its pros and cons, and others on this forum may have suggestions, too. If you are interested in kayaking, call Adventures Through Kayaking at (888) 900-3015 and talk with them about sea kayaking. And if you go in July you can often see baby seals.
Some of the must see attractions are Hurricane Ridge, the Hoh Rain Forest, Rialto and Second Beaches, and Lake Crescent.
If you enjoy visiting farms, as well as superb fresh food, visit Dungeness Valley Creamery, Christy Johnston's Family Farm, and Nash Huber's farm stand. They are all close to each other in the Dungeness region of Sequim. The dairy has adorable calves and raw Jersey milk that has to be tasted to be believed. Make sure you get local strawberries and raspberries; you may be able to pick your own. You can combine a trip to these farms with a peaceful, pastoral, stroll along the Dungeness River Dike Trail or a visit to the Dungeness Spit.
Try for a swim in Lake Crescent at East Beach, or, if you are daring, hike along the Spruce Rail Road Trail and enter Lake Crescent at the cold but lovely Devil's Punchbowl.
You'll have a wonderful time out there. It's paradise on earth.
Hope my answer has been helfpul!
Try using the "build your trip" flight comparsion tool here:
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Links of interest:
Olympic Rain Forest Olympic Mountains Washington State Parks