Fall and spring are great. Usually before school end and after school starts again. USFS CGs don't open until Memorial Day and close Mid September to early October. State Parks are open all year. Some part of Mt Rainier National Parks are open until late October. Some of Olympic National Park on the coast are open all year long. Also parks on Lake CUSHMAN are open all year. Early June could be cold and October could be rainy. July thru August may need a reservation unless you get in on Sunday morning for Walk up site. Mid week also may be lucky at state parks. Don't plan on getting a site on Friday or Saturday without a reservation, July-August. Washington has some really good weather in September if you hit it right. Check the reservation system RECREATION.GOV to get a feel on if the park is full.