Olympic National Park
Here is a map of Olympic National Park. You can click on it to go to the park website.
One thing to know about the park is there are no roads that go through the middle. There's only one big long road all the way around. Also, to get there from Seattle either means you take the ferry or you drive south quite a ways to get down to where the peninsula connects with the rest of the state. You at least have to stay overnight. But two days is enough to see most of the park, unless you want to go hiking.
Taking the ferry has the added bonus of putting you on one of the islands. Some of these islands are nice to explore by themselves. And they are typically where you would charter a whale watching tour. Whale watching tours are mostly for Orcas, so not technically whales, but the benefit with Orcas is that they pop up out of the water far more often. There is an island called Orcas Island that is actually most well known for having the highest peak in the surrounding area and you can see really far. And you can drive up to the top.
Basically everything you need to know about the park is here.
One thing worth mentioning if you're a Twilight fan. Twilight is supposed to happen in the town of Forks, which is on the far west side of the Olympic Peninsula. It's not actually filmed there but the town has a lot of Twilight-themed stuff there. You pass through Forks on your way around the peninsula.