Avoid driving on i90 and through/near Seattle, too much traffic. I'd either go to the olympic peninsula then take the ferry to Bellingham and take hw20 across the mountains, go to Leavenworth, and see Rainer on your way back. Or drive down south from the Olympics, over hw12, stopping at Umtanum Creek Recreation Site, then going on to Leavenworth.

Overall your trip is doable but I would give yourself a little more time, or either spend your time at the coast or in the mountains.

You'll have no issue finding plenty of hikes <10 miles, not sure what you're used to but 10 miles here can be a grueling all day hike. In order to access most of the public lands you'll need to get yourself a Discover Pass, and possibly a North West Forest Pass, depends on the area.

The Olympics are a rain forest so bring rain gear.