It's rarely the fires themselves that prevent access--oftentimes they are burning in less accessible areas that affect a specific system of trails far from the frequently used trailheads. For example, last year the PCT was closed near the Canadian border. The bigger problem is smoke making the hiking unpleasant and obscuring the views. The smoke might be from local fires as it was last year, or from fires in Canada, Montana, etc--the effect can be the same. If there are smoke issues, there are smoke forecasts and predictions you can look at to see which areas are relatively clear.

Sure, this was taken near Panorama Point, which is the high point of the Skyline Trail in Mount Rainier National Park. It's a beautiful loop trail that starts from the Paradise area and is the most popular hike in the park. The distant volcano is Mount Adams and the taller of the double peaks poking out of the clouds is Unicorn Peak.

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Here's a view on a clear day when I googled "view from panorama point rainier"

Have you explored much terrain above tree level? For a burly outing in a beautiful volcanic alpine environment with striking cliffs and sweeping seemingly barren landscapes check out the Observation Rock and Echo Rock areas in late Summer. I have not needed special gear beyond trekking poles and maybe microspikes. Approach via Knapsack Pass for an adventurous long day. Proceed a few hundred feet up the ridge above Observation Rock for incredible views of Rainier's Mowich Face. There are other cool areas like this around Rainier.

Deception Pass and surroundings have unique rocky bald habitats.

The Cascade Mountains in Washington are consistently the snowiest places in the country, at least where officially measured. Mount Baker ski area holds the world record for highest recorded snowfall for a season. Stevens Pass, the nearest ski resort to Plain, averages 460 inches of snow per year. It is true that it snows very little in the cities along Puget Sound where most people live as warmer air off the ocean moderates temperatures. But even close the Ocean there are glaciers in the Olympic Mountains.

https://en.m.wikipedia.org/wiki/List_of_snowiest_places_in_the_United_States_by_state

That's plenty of time to see all the various ecosystems of the park. If you want to hike around in the high country, or visit Rainier or other equally beautiful parts of the Cascades, then definitely try to come in July at the earliest. If you're fit hikers and want to do an all-day hike, then the High Divide - 7 Lakes Basin loop is a great choice. That's definitely a July hike. Check out wta.org for more hike suggestions, and consider posing questions/doing research at NW Hikers as well.

The classic short trip to ONP is some combination of Hurricane Ridge/a beach/Hoh Rainforest. You'll have more time so definitely go deeper than that. Forks is a good gateway to the Hoh and some coastal areas but is a pretty run down place with not much to do.

Port Angeles area will have most lodging options and is a good town to stay in but it's much closer to the Hurricane Ridge area and the northern Olympics than to the coast (check out Grand Ridge and Royal Basin for a great long hikes in the northern Olys). Just check out drive times from there to places you wanna visit.

Fly into SeaTac and consider taking the ferry from Seattle or Edmonds to get across the sound to add some novelty to the journey, but you can also just drive around through Tacoma.

Go anyway to have a look at the river, it's cool to see it running high, and if you come to a flooded area go check out Rattlesnake Lake down the road, Little Si, or the Tiger Mountain area.