Decide in advance what you would like to see. This is a big park, and no roads go completely through it. The roads that do venture inside (and they're major tourist attractions) are generally short and pleasant. It's 19 miles from U.S. 101 to the Hoh Visitor Center, and 17 miles to Hurricane Ridge.
If you want to see the rainforests and the coastal strip, drive north from Aberdeen on U.S. 101 (which circumnavigates the peninsula) through the coastal region, perhaps stopping at the Kalaloch Information Station and Ruby Beach, and then head to the Hoh Rain Forest Visitor Center, from where you can explore further. To see the glaciers and the alpine meadows of the east side of the park, start by driving to the Olympic National Park Visitor Center in Port Angeles, and from there head up to Hurricane Ridge, where you set out on a hike or drive even farther into the park. From Seattle, the eastern option is closer.
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.