Overnight in Olympic National Park

Hi, my coworker and I are going to be in Seattle the last week of June for a work function. We want to get some hiking and camping in while we are there and Olympic is our goal. We also would like to keep it on a budget so public transportation (I've found a bus that goes from seatac to port angeles?) is preferred but will rent a car if the money isnt that different.
Going along the coast is also preferred.
Backcountry camping would be nice, but established campgrounds are fine.

I've gotten some ideas from other threads and the park website, but for the Pacific Northwesters out there, whats the one thing you would have to see if you went out there and you only had about 1.5 days?

Thanks for the help!