OK, I'm local, and I just got thru taking in all the tourist stuff with visiting family over the holidays. Here's my $0.02 worth:
For "in city" hotels I usually recommend the W or the Sheraton. The W because it's on the monorail line and gets you around without having to use a taxi/Uber, and the Sheraton because it's an easy walk to Pike St Market and/or the convention center. But my favorite is the Arctic Club, which is close to both Pioneer Square and the International District.
For a more "local" place it depends. I'm not really sold on Ballard, in my opinion Magnolia's nicer, but that's pretty close in. Fremont would be my choice also if placed up to Ballard, but that's because it's a much more walk-able neighborhood. I'll suggest West Seattle, because it's more small town, distinct from downtown both culturally and physically, and because if you can get a place facing Elliot Bay the views can be amazing as the city lights up. Plus you have an excuse to use the water taxi across the bay. Another choice would be a place around Green Lake, but NOT on 99.
I've never stayed in Marblemount, but I used to run away on weekends just up the road to Lake Diablo and get a cabin there. We'd play on the lake, and hike locally. There are a lot of turnouts on the road going up there, and you can park in one and walk down to the river and all over the canyon. It's great for quiet, undisturbed picnicking.
In the Olympics you'll find everyone hikes Hurricane Ridge. It's more like a city sidewalk for traffic. Nice easy hike though.
I'll let you in on a secret: drive an hour west to La Push. Then take the road to Second Beach and hike that out to the water. Fantastic! and if you really want to stretch the legs and be alone, go a couple more miles down the trail to Third Beach. Picture postcard scenery. Take food and water, and a rain jacket!
Other than just hiking around, I recommend you take an afternoon and visit Port Townsend. Google it.
In town stuff to do? I'll recommend the following:
Pike St Market/the waterfront/Pioneer Square - You can easily do all these in a day, and that encompasses the Art Museum, the Aquarium, etc. They are all in walking distance of each other. You cannot do it all, but leave some for next time.
The Space Needle/The Museum of Pop Culture/The Glass Gardens - This is another day in itself, and more if you throw in the Pacific Science Center. It can take a couple hours to get up to the top of the Space Needle due to lines, and summer is peak tourist season. The Museums also are time issued tickets, so you can only enter within the 1/2 hour segment you choose.
You're going to miss the best weekend open markets (Fremont & Edmonds) because they are Saturdays only, but Fremont is worth walking around. If you add in the Burke (at UW) or kayaking Lake Union that's a full day.
If you like old airplanes you have choices, and if you like old cars you have more. Boeing's Museum of Flight, The FHC Museum at Paine Field, the LeMay Car Museum in Tacoma, and the LeMay family collection just down the road in Parkland. (LeMay liked his cars.)
If you like Asian Food I suggest the International District (KauKau BBQ is a favorite of mine), and you can easy lose track of time at the Pinball Museum just down the block.
If the weather's good take a lunch and go sit at one of the tables at Daybreak Star, odds are you'd be the only one there. And you have a fantastic view up the Sound to Mt Adams and can watch the sailboat races. Often can see/hear sea lions too. There are a number of good hikes in that park, the most popular being down to the lighthouse.
Don't forget: In August the sun is up at 0500 and it gets dark around 2200. It's the dry/warm time of year but it can rain. A light rain jacket and hat are normal accessories, everyone wears shorts, and nobody carries an umbrella.