As an NPS Park Ranger in the summer at Mesa Verde N.P. ( I know that its too far to go from Seattle for a weekend) I would highly recommend Olympic NP. Because Olympic has such diversity and there is no central, trans-park hwy, I would recommend Elwah Dam RV Park outside Port Angeles. Elwha Dam RV Park
I like this park because of the staff and its proximity to a number of Park entrances.
Check out the Park website; Olympic National Park - Olympic National Park
Download the park map.
There is so much diversity, you can make forays into the park at many different places and never see the same thing twice.
I hope you enjoy the National Parks!