As a wilderness park, mechanized transport is limited. That is, forget the wheels.
However, 168 miles of roads (69 of which are gravel) provide vehicle access to various points around the park. All park roads are "spur roads" off U.S. Highway 10no roads cross the Olympic wilderness. While not in the park itself, a spectacular nearby drive is to the end of Route 112, which takes you to the end of Cape Flattery. Between the months of March and May you could catch sight of whales off the coast. Any time of year you'll see pulse-racing blufftop views of the Strait of Juan de Fuca and Tatoosh Islands.