Depends on how far you want to go, but check out Deception Pass state park. They have year round camping. The loop open this time of year is forested and fairly protected from the wind.

There is a lot to do in Washington. We have three National Parks: Mt Rainier, Olympic, and North Cascades. Olympic has many easy trails in the rainforest and on the wilderness coast that are beautiful, accessible in June, and mostly flat. In addition to the natural parks, there is a huge amount of wilderness protected land and national forest that have gorgeous features. There is whale watching as well in the Salish Sea. Washington is home to many exceptional viticultural regions if you're into wine. Seattle itself has a great variety of museums, restaurants, and markets. Eastern Washington has beautiful state parks, dry rivers, scablands, recreational lakes, and more. It really depends on what you like doing.

Yeah, this shot is impossible to get. The core appears SW, while to get this shot OP would need to shoot Hood facing NNE.

While this is a lovely waterfall in Olympic National Park, it is not in the Hoh Rainforest, which is located south of The Sol Duc River valley, and is about a two hour drive away.

Edit: Hoh