The Olympic was and remains the "grand dame" of Seattle hotels, but for a one-night stay I'd go with the Mayflower. Assuming you won't have a car until you leave for ONP, the Mayflower's location, basically next door to the Westlake light rail station is a major plus (direct train to/from the airport) and it's also closer to places like the Pike Place market, monorail to Seattle Center, etc. The hotel itself is lovely, with excellent service, and the on-site restaurant, Andaluca, is very good if you want to limit your wandering about.
Going to Olympic National Park next month? Yikes. Bring your Wellies and a brolly.
Meant to add, the hotel's bar is called "Oliver's."